answers (anticipation guide and lesson 7-1) · 2019-02-12 · skills practice multiplying monomials...
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Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
An
tici
pati
on
Gu
ide
Po
lyn
om
ials
B
efo
re y
ou
beg
in C
ha
pte
r 7
•
R
ead
each
sta
tem
en
t.
•
D
eci
de w
heth
er
you
Agre
e (
A)
or
Dis
agre
e (
D)
wit
h t
he s
tate
men
t.
•
W
rite
A o
r D
in
th
e f
irst
colu
mn
OR
if
you
are
not
sure
wh
eth
er
you
agre
e o
r d
isagre
e,
wri
te N
S (
Not
Su
re).
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
Wh
en
mu
ltip
lyin
g t
wo p
ow
ers
th
at
have t
he s
am
e b
ase
, m
ult
iply
th
e e
xp
on
en
ts.
D
2.
( k 3 ) 4
is
equ
ivale
nt
to k
12 .
A
3.
To d
ivid
e t
wo p
ow
ers
th
at
have t
he s
am
e b
ase
, su
btr
act
th
e e
xp
on
en
ts.
A
4.
( 2 −
5 ) 3
is
the s
am
e a
s 2
−
5 3
.D
5.
A p
oly
nom
ial
may c
on
tain
on
e o
r m
ore
mon
om
ials
.A
6.
Th
e d
egre
e o
f th
e p
oly
nom
ial
3 x 2 y 3 -
5y 2 +
8 x 3 i
s 3 b
eca
use
th
e
hig
hest
exp
on
en
t is
3.
D
7.
Th
e s
um
of
the t
wo p
oly
nom
ials
(3 x 2 y -
4x y 2 +
2y 3 )
an
d
(6x y 2 +
2x 2 y -
7)
in s
imp
lest
form
is
5x 2 y +
2xy 2 +
2y 3 -
7.
A
8.
(4m
2 +
2m
- 3
) -
(m
2 -
m +
3)
is e
qu
al
to 3
m 2 +
m.
D
9.
Beca
use
th
ere
are
dif
fere
nt
exp
on
en
ts i
n e
ach
fact
or,
th
e
dis
trib
uti
ve p
rop
ert
y c
an
not
be u
sed
to m
ult
iply
3n
3 b
y
(2n
2 +
4n
- 1
2).
D
10.
Th
e F
OIL
meth
od
of
mu
ltip
lyin
g t
wo b
inom
ials
sta
nd
s fo
r F
irst
, O
ute
r, I
nn
er,
La
st.
A
11.
Th
e s
qu
are
of
r +
t,
(r +
t) 2
, w
ill
alw
ays
equ
al
r 2 +
t 2 .
D
12.
Th
e p
rod
uct
of
(x +
y)
an
d (
x -
y)
wil
l alw
ays
equ
al
x 2 -
y 2 .
A
A
fter y
ou
com
ple
te C
ha
pte
r 7
•
R
ere
ad
each
sta
tem
en
t an
d c
om
ple
te t
he l
ast
colu
mn
by e
nte
rin
g a
n A
or
a D
.
•
D
id a
ny o
f you
r op
inio
ns
abou
t th
e s
tate
men
ts c
han
ge f
rom
th
e f
irst
colu
mn
?
•
F
or
those
sta
tem
en
ts t
hat
you
mark
wit
h a
D,
use
a p
iece
of
pap
er
to w
rite
an
exam
ple
of
wh
y y
ou
dis
agre
e.
7
Ch
ap
ter
7
3
Gle
ncoe A
lgeb
ra 1
Ste
p 1
Ste
p 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-1
Ch
ap
ter
7
5
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Mu
ltip
lyin
g M
on
om
ials
Mo
no
mia
ls
A m
on
om
ial
is a
nu
mber,
a v
ari
able
, or
the p
rod
uct
of
a n
um
ber
an
d o
ne o
r m
ore
vari
able
s w
ith
non
negati
ve i
nte
ger
exp
on
en
ts.
An
exp
ress
ion
of
the f
orm
xn i
s ca
lled
a
po
wer a
nd
rep
rese
nts
th
e p
rod
uct
you
obta
in w
hen
x i
s u
sed
as
a f
act
or
n t
imes.
To m
ult
iply
tw
o p
ow
ers
th
at
have t
he s
am
e b
ase
, ad
d t
he e
xp
on
en
ts.
Pro
du
ct
of
Po
wers
For
any n
um
ber
a a
nd a
ll in
tegers
m a
nd n
, a
m ․
an =
am
+ n.
S
imp
lify
(3
x6)(
5x
2).
(3x
6)(
5x
2) =
(3)(
5)(
x6 ․
x2)
Gro
up t
he c
oeffic
ients
and t
he v
ariable
s
=
(3 ․
5)(
x6
+ 2)
Pro
duct
of
Pow
ers
=
15x
8
Sim
plif
y.
Th
e p
rod
uct
is
15x
8.
S
imp
lify
(-
4a
3b
)(3a
2b
5).
(-4a
3b)(
3a
2b
5) =
(-
4)(
3)(
a3 ․
a2)(
b ․
b5)
=
-12(a
3 +
2)(
b1
+ 5)
=
-12a
5b
6
Th
e p
rod
uct
is -
12
a5b
6.
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. y(y
5)
2. n
2 ․
n7
3. (-
7x
2)(
x4)
y
6
n
9
-
7x
6
4. x(x
2)(
x4)
5. m
․ m
5
6. (-
x3)(-
x4)
x
7
m
6
x
7
7. (2
a2)(
8a
) 8
. (r
s)(r
n3)(
n2)
9. (x
2y)(
4xy
3)
1
6a
3
r2
n6
4
x3y
4
10. 1
−
3 ( 2
a 3 b)(
6b 3 )
11. (-
4x
3)(-
5x
7)
12. (-
3j2
k4)(
2jk
6)
4
a3b
4
20x
10
-
6j3
k1
0
13. ( 5
a 2 bc 3 ) ( 1
−
5 a
bc 4 )
14. (-
5xy)(
4x
2)(
y4)
15. (1
0x
3yz2
)(-
2xy
5z)
a
3b
2c
7
-
20x
3y
5
-
20x
4y
6z
3
7-1
Exam
ple
1Exam
ple
2
Answers (Anticipation Guide and Lesson 7-1)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
6
Gle
ncoe A
lgeb
ra 1
Sim
plify
Exp
ress
ion
s A
n e
xp
ress
ion
of
the f
orm
(x
m)n
is
call
ed
a p
ow
er o
f a
po
wer
an
d r
ep
rese
nts
th
e p
rod
uct
you
obta
in w
hen
xm i
s u
sed
as
a f
act
or
n t
imes.
To f
ind
th
e
pow
er
of
a p
ow
er,
mu
ltip
ly e
xp
on
en
ts.
Po
wer
of
a P
ow
er
For
any n
um
ber
a a
nd a
ll in
tegers
m a
nd n
, (a
m)n
= a
mn.
Po
wer
of
a P
rod
uct
For
any n
um
ber
a a
nd a
ll in
tegers
m a
nd n
, (a
b)m
= a
mb
m.
We c
an
com
bin
e a
nd
use
th
ese
pro
pert
ies
to s
imp
lify
exp
ress
ion
s in
volv
ing m
on
om
ials
.
S
imp
lify
(-
2ab
2)3
(a2)4
.
(-2a
b2)3
(a2)4
= (-
2a
b2)3
(a8)
Pow
er
of
a P
ow
er
=
(-
2)3
(a3)(
b2)3
(a8)
Pow
er
of
a P
roduct
=
(-
2)3
(a3)(
a8)(
b2)3
G
roup t
he c
oeffic
ients
and t
he v
ariable
s
=
(-
2)3
(a1
1)(
b2)3
P
roduct
of
Pow
ers
=
-8
a1
1b
6
Pow
er
of
a P
ow
er
Th
e p
rod
uct
is -
8a
11b
6.
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
1. (y
5)2
2
. (n
7)4
3. (x
2)5
(x3)
y
10
n2
8
x1
3
4. -
3(a
b4)3
5. (-
3a
b4)3
6. (4
x2b
)3
-
3a
3b
12
-27
a3b
12
64
x6b
3
7. (4
a2)2
(b3)
8. (4
x)2
(b3)
9. (x
2y
4)5
1
6a
4b
3
16x
2b
3
x1
0y
20
10. (2
a3b
2)(
b3)2
11. (-
4xy)3
(-2x
2)3
12. (-
3j2
k3)2
(2j2
k)3
2
a3b
8
512
x9y
3
72j1
0k
9
13. (2
5 a
2 b) 3
( 1 −
5 a
bf ) 2
14. (2
xy)2
(-3
x2)(
4y
4)
15. (2
x3y
2z2
)3(x
2z)
4
6
25a
8b
5f2
-
48x
4y
6
8x
17y
6z
10
16. (-
2n
6y
5)(-
6n
3y
2)(
ny)3
17. (-
3a
3n
4)(-
3a
3n
)4
18. -
3(2
x)4
(4x
5y)2
1
2n
12y
10
-243a
15n
8
-768
x1
4y
2
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Mu
ltip
lyin
g M
on
om
ials
7-1 Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-1
Ch
ap
ter
7
7
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Mu
ltip
lyin
g M
on
om
ials
Dete
rm
ine w
heth
er e
ach
ex
pressio
n i
s a
mo
no
mia
l. W
rit
e yes o
r no
. E
xp
lain
.
1. 11 Y
es;
11 i
s a
real
nu
mb
er
an
d a
n e
xam
ple
of
a c
on
sta
nt.
2. a
- b
N
o;
this
is t
he d
iffe
ren
ce,
no
t th
e p
rod
uct,
of
two
vari
ab
les.
3. p
2 −
r 2 N
o;
this
is t
he q
uo
tien
t, n
ot
the p
rod
uct,
of
two
vari
ab
les.
4. y Y
es;
sin
gle
vari
ab
les a
re m
on
om
ials
.
5. j3
k Y
es;
this
is t
he p
rod
uct
of
two
vari
ab
les.
6. 2
a +
3b N
o;
this
is t
he s
um
of
two
mo
no
mia
ls.
Sim
pli
fy.
7. a
2(a
3)(
a6)
a1
1
8. x(x
2)(
x7)
x1
0
9. (y
2z)
(yz2
) y
3z
3
10. (ℓ
2k
2)(
ℓ3k
) �
5k
3
11. (a
2b
4)(
a2b
2)
a4b
6
12. (c
d2)(
c3d
2)
c4d
4
13. (2
x2)(
3x
5)
6x
7
14. (5
a7)(
4a
2)
20a
9
15. (4
xy
3)(
3x
3y
5)
12
x4y 8
16. (7
a5b
2)(
a2b
3)
7a
7b
5
17. (-
5m
3)(
3m
8) -
15
m1
1
18. (-
2c4
d)(-
4cd
) 8
c5d
2
19. (1
02)3
10
6 o
r 1,0
00,0
00
20. (p
3)1
2 p
36
21. (-
6p
)2 36p
2
22. (-
3y)3
-
27
y3
23. (3
pr2
)2 9p
2r4
24. (2
b3c4
)2 4
b6c
8
GEO
METR
Y E
xp
ress t
he a
rea
of
ea
ch
fig
ure a
s a
mo
no
mia
l.
25.
x2
x5
26.
cd
cd
27.
4p 9
p3
x
7
c
2d
2
18
p4
7-1
Answers (Lesson 7-1)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
8
Gle
ncoe A
lgeb
ra 1
Practi
ce
Mu
ltip
lyin
g M
on
om
ials
Dete
rm
ine w
heth
er e
ach
ex
pressio
n i
s a
mo
no
mia
l. W
rit
e yes o
r no
. E
xp
lain
yo
ur
rea
so
nin
g.
1. 2
1 a
2
−
7b N
o;
this
in
vo
lves t
he q
uo
tien
t, n
ot
the p
rod
uct,
of
vari
ab
les.
2. b
3 c 2
−
2
Y
es;
this
is t
he p
rod
uct
of
a n
um
ber,
1
−
2 ,
an
d t
wo
vari
ab
les.
Sim
pli
fy e
ach
ex
pressio
n.
3. (-
5x
2y)(
3x
4)
-15
x6y
4. (2
ab
2f
2)(
4a
3b
2f
2)
8a
4b
4f4
5. (3
ad
4)(
-2
a2)
-6
a3d
4
6. (4
g3h
)(-
2g
5)
-8
g8h
7. (-
15x y 4 ) (-
1
−
3 x
y 3 ) 5
x2y
7
8. (-
xy)3
(xz)
-
x4y
3z
9. (-
18 m
2 n
) 2 (-
1
−
6 m
n 2 ) -
54m
5n
4
10. (0
.2a
2b
3)2
0.0
4a
4b
6
11.
( 2
−
3 p
) 2
4
−
9 p
2
12.
( 1
−
4 a
d 3 ) 2
1
−
16 a
2 d
6
13. (0
.4k
3)3
0.0
64k
9
14. [(
42)2
]2 4
8 o
r 65,5
36
GEO
METR
Y E
xp
ress t
he a
rea
of
ea
ch
fig
ure a
s a
mo
no
mia
l.
15.
6a2
b4
3ab
2
16.
5x3
17.
6ab
3
4a2
b
1
8a
3b
6
(25
x6)π
1
2a
3b
4
GEO
METR
Y E
xp
ress t
he v
olu
me o
f ea
ch
so
lid
as a
mo
no
mia
l.
18.
3h2
3h2
3h2
19.
m3n
mn3
n
20.
7g2
3g
2
7h
6
m4n
5
(63
g4)π
21. C
OU
NTIN
G A
pan
el
of
fou
r li
gh
t sw
itch
es
can
be s
et
in 2
4 w
ays.
A p
an
el
of
five l
igh
t sw
itch
es
can
set
in t
wic
e t
his
man
y w
ays.
In
how
man
y w
ays
can
fiv
e l
igh
t sw
itch
es
be s
et?
2
5 o
r 32
22. H
OB
BIE
S T
aw
a w
an
ts t
o i
ncr
ease
her
rock
coll
ect
ion
by a
pow
er
of
thre
e t
his
year
an
d
then
in
crease
it
again
by a
pow
er
of
two n
ext
year.
If
she h
as
2 r
ock
s n
ow
, h
ow
man
y
rock
s w
ill
she h
ave a
fter
the s
eco
nd
year?
2
6 o
r 64
7-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-1
Ch
ap
ter
7
9
Gle
ncoe A
lgeb
ra 1
1. G
RA
VIT
Y A
n e
gg t
hat
has
been
fall
ing
for
x s
eco
nd
s h
as
dro
pp
ed
at
an
avera
ge
speed
of
16
x f
eet
per
seco
nd
. If
th
e e
gg i
s d
rop
ped
fro
m t
he t
op
of
a b
uil
din
g,
its
tota
l d
ista
nce
tra
vele
d i
s th
e p
rod
uct
of
the a
vera
ge r
ate
tim
es
the t
ime.
Wri
te a
si
mp
lifi
ed
exp
ress
ion
to s
how
th
e
dis
tan
ce t
he e
gg h
as
travele
d a
fter
x
seco
nd
s.
2. C
IVIL
EN
GIN
EER
ING
A
develo
per
is
pla
nn
ing a
sid
ew
alk
for
a n
ew
d
evelo
pm
en
t. T
he s
idew
alk
can
be
inst
all
ed
in
rect
an
gu
lar
sect
ion
s th
at
have a
fix
ed
wid
th o
f 3 f
eet
an
d a
len
gth
th
at
can
vary
. A
ssu
min
g t
hat
each
se
ctio
n i
s th
e s
am
e l
en
gth
, exp
ress
th
e
are
a o
f a 4
-sect
ion
sid
ew
alk
as
a
mon
om
ial.
x
3 f
t
3. PR
OB
AB
ILIT
Y If
you
fli
p a
coin
3 t
imes
in a
row
, th
ere
are
23 o
utc
om
es
that
can
occ
ur.
Ou
tco
mes
HH
HT
TT
HT
TT
HH
HT
HT
TH
HH
TT
HT
If
you
th
en
fli
p t
he c
oin
tw
o m
ore
tim
es,
th
ere
are
23 ×
22 o
utc
om
es
that
can
occ
ur.
How
man
y o
utc
om
es
can
occ
ur
if
you
fli
p t
he q
uart
er
as
men
tion
ed
above
plu
s fo
ur
more
tim
es?
Wri
te y
ou
r an
swer
in t
he f
orm
2x.
4. SPO
RTS
T
he v
olu
me o
f a s
ph
ere
is
giv
en
by t
he f
orm
ula
V=
4 − 3 π
r 3 ,
wh
ere
r i
s th
e
rad
ius
of
the s
ph
ere
. F
ind
th
e v
olu
me o
f air
in
th
ree d
iffe
ren
t bask
etb
all
s. U
se
π=
3.1
4.
Rou
nd
you
r an
swers
to t
he
neare
st w
hole
nu
mber.
Ball
Rad
ius (
in.)
Vo
lum
e (
in3)
Child
’s4
268
Wom
en’s
4.5
382
HT
H4.8
463
So
urce:
Wik
iAnsw
ers
5. ELEC
TR
ICIT
Y A
n e
lect
rici
an
use
s th
e
form
ula
W =
I2R
, w
here
W i
s th
e p
ow
er
in w
att
s, I
is
the c
urr
en
t in
am
pere
s, a
nd
R
is
the r
esi
stan
ce i
n o
hm
s.
a
. F
ind
th
e p
ow
er
in a
hou
seh
old
cir
cuit
th
at
has
20 a
mp
ere
s of
curr
en
t an
d
5 o
hm
s of
resi
stan
ce.
b
. If
th
e c
urr
en
t is
red
uce
d b
y o
ne h
alf
, w
hat
hap
pen
s to
th
e p
ow
er?
Th
e p
ow
er
is o
ne-f
ou
rth
th
e
pre
vio
us a
mo
un
t.
Wo
rd
Pro
ble
m P
racti
ce
Mu
ltip
lyin
g M
on
om
ials
7-1
16
x2
12
x
29
2000 w
att
s
Answers (Lesson 7-1)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
10
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
An
Wan
g
An
Wan
g (
1920–1990)
was
an
Asi
an
-Am
eri
can
wh
o b
eca
me o
ne o
f th
e p
ion
eers
of
the
com
pu
ter
ind
ust
ry i
n t
he U
nit
ed
Sta
tes.
He g
rew
up
in
Sh
an
gh
ai,
Ch
ina,
bu
t ca
me t
o t
he
Un
ited
Sta
tes
to f
urt
her
his
stu
die
s in
sci
en
ce.
In 1
948,
he i
nven
ted
a m
agn
eti
c p
uls
e
con
troll
ing d
evic
e t
hat
vast
ly i
ncr
ease
d t
he s
tora
ge c
ap
aci
ty o
f co
mp
ute
rs.
He l
ate
r fo
un
ded
h
is o
wn
com
pan
y,
Wan
g L
abora
tori
es,
an
d b
eca
me a
lead
er
in t
he d
evelo
pm
en
t of
desk
top
ca
lcu
lato
rs a
nd
word
pro
cess
ing s
yst
em
s. I
n 1
988,
Wan
g w
as
ele
cted
to t
he N
ati
on
al
Inven
tors
Hall
of
Fam
e.
Dig
ital
com
pu
ters
sto
re i
nfo
rmati
on
as
nu
mbers
. B
eca
use
th
e e
lect
ron
ic c
ircu
its
of
a
com
pu
ter
can
exis
t in
on
ly o
ne o
f tw
o s
tate
s, o
pen
or
close
d,
the n
um
bers
th
at
are
sto
red
can
co
nsi
st o
f on
ly t
wo d
igit
s, 0
or
1.
Nu
mbers
wri
tten
usi
ng o
nly
th
ese
tw
o d
igit
s are
call
ed
b
ina
ry
nu
mb
ers.
To f
ind
th
e d
eci
mal
valu
e o
f a b
inary
nu
mber,
you
use
th
e d
igit
s to
wri
te
a p
oly
nom
ial
in 2
. F
or
inst
an
ce,
this
is
how
to f
ind
th
e d
eci
mal
valu
e o
f th
e n
um
ber
1001101
2.
(Th
e s
ubsc
rip
t 2 i
nd
icate
s th
at
this
is
a b
inary
nu
mber.
)
1001101
2 =
1 ×
26 +
0 ×
25 +
0 ×
24 +
1 ×
23 +
1 ×
22 +
0 ×
21 +
1 ×
20
= 1
× 6
4 +
0 ×
32 +
0 ×
16
+ 1
× 8
+ 1
× 4
+ 0
× 2
+ 1
× 1
=
64
+
0
+
0
+
8
+
4
+
0
+
1
= 7
7
Fin
d t
he d
ecim
al
va
lue o
f ea
ch
bin
ary
nu
mb
er.
1.
1111
2 15
2.
10000
2 16
3.
11000011
2 195
4.
10111001
2 185
Writ
e e
ach
decim
al
nu
mb
er a
s a
bin
ary
nu
mb
er.
5.
8 1000
2
6.
11 1011
2
7.
29
11101
2
8.
117 1110101
2
9.
Th
e c
hart
at
the r
igh
t sh
ow
s a s
et
of
deci
mal
cod
e n
um
bers
th
at
is u
sed
wid
ely
in
sto
rin
g
lett
ers
of
the a
lph
abet
in a
com
pu
ter’
s m
em
ory
. F
ind
th
e c
od
e n
um
bers
for
the l
ett
ers
of
you
r n
am
e.
Th
en
wri
te t
he c
od
e f
or
you
r n
am
e
usi
ng b
inary
nu
mbers
. A
nsw
ers
will
vary
.
7-1
Th
e A
meri
can
Sta
nd
ard
Gu
ide f
or
Info
rmati
on
In
terc
han
ge (
AS
CII)
A
65
N
78
a
97
n
110
B
66
O
79
b
98
o
111
C
67
P
80
c
99
p
112
D
68
Q
81
d
100
q
113
E
69
R
82
e
101
r 114
F
70
S
83
f 102
s
115
G
71
T
84
g
103
t 116
H
72
U
85
h
104
u
117
I 73
V
86
i 105
v
118
J
74
W
87
j 106
w
119
K
75
X
88
k
107
x
120
L
76
Y
89
l 108
y
121
M
77
Z
90
m
10
9z
122
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-2
Ch
ap
ter
7
11
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Div
idin
g M
on
om
ials
Qu
oti
en
ts o
f M
on
om
ials
T
o d
ivid
e t
wo p
ow
ers
wit
h t
he s
am
e b
ase
, su
btr
act
th
e
exp
on
en
ts.
Qu
oti
en
t o
f P
ow
ers
For
all
inte
gers
m a
nd n
and a
ny n
onzero
num
ber
a,
a m −
a n =
a m-
n .
Po
wer
of
a Q
uo
tien
tF
or
any inte
ger
m a
nd a
ny r
eal num
bers
a a
nd
b,
b ≠
0,
( a
−
b ) m
= a
m −
b m .
S
imp
lify
a 4 b
7
−
ab
2
. A
ssu
me
tha
t n
o d
en
om
ina
tor e
qu
als
zero
.
a 4 b 7 −
ab 2 =
( a 4 −
a ) (
b 7 −
b 2 )
Gro
up p
ow
ers
with t
he s
am
e b
ase.
=
(a
4 -
1)(
b7
- 2)
Quotient
of
Pow
ers
=
a3b
5
Sim
plif
y.
Th
e q
uoti
en
t is
a3b
5 .
S
imp
lify
( 2 a
3 b
5
−
3 b
2 ) 3
. A
ssu
me
tha
t n
o d
en
om
ina
tor e
qu
als
zero
.
( 2 a
3 b 5 −
3 b 2 ) 3
= (2
a 3 b 5 ) 3
−
(3 b 2 ) 3
Pow
er
of
a Q
uotient
=
2 3 ( a
3 ) 3
( b 5 ) 3
−
(3 ) 3
( b 2 ) 3
Pow
er
of
a P
roduct
=
8 a
9 b 1
5 −
27 b 6
Pow
er
of
a P
ow
er
=
8 a
9 b 9 −
27
Q
uotient
of
Pow
ers
Th
e q
uoti
en
t is
8 a
9 b 9 −
27
.
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
Assu
me t
ha
t n
o d
en
om
ina
tor e
qu
als
zero
.
1. 5
5 −
5 2 5
3 o
r 125
2. m
6 −
m 4 m
2
3. p
5 n
4 −
p 2 n
p3n
3
4. a
2 −
a
a
5. x
5 y 3 −
x 5 y 2
y
6. -
2 y 7 −
14 y 5
- 1
−
7 y
2
7. x
y 6 −
y 4 x y
2
8. ( 2
a 2 b −
a
) 3
8a
3b
3
9. ( 4
p 4 r 4 −
3 p
2 r 2 ) 3
6
4
−
27 p
6 r 6
10. ( 2
r 5 w
3 −
r 4 w
3 ) 4
16r 4
11. ( 3
r 6 n
3 −
2 r 5 n ) 4
8
1
−
16 r
4 n
8
12. r
7 n
7 t 2
−
n 3 r 3 t 2
r 4
n4
7-2
Exam
ple
1Exam
ple
2
Answers (Lesson 7-1 and Lesson 7-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
12
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Div
idin
g M
on
om
ials
Neg
ati
ve E
xp
on
en
ts
An
y n
on
zero
nu
mber
rais
ed
to t
he z
ero
pow
er
is 1
; fo
r exam
ple
, (-
0.5
)0 =
1.
An
y n
on
zero
nu
mber
rais
ed
to a
negati
ve p
ow
er
is e
qu
al
to t
he r
eci
pro
cal
of
the
nu
mber
rais
ed
to t
he o
pp
osi
te p
ow
er;
for
exam
ple
, 6
-3 =
1 −
6 3 .
Th
ese
defi
nit
ion
s ca
n b
e u
sed
to
sim
pli
fy e
xp
ress
ion
s th
at
have n
egati
ve e
xp
on
en
ts.
Zero
Exp
on
en
tF
or
any n
onzero
num
ber
a,
a0 =
1.
Neg
ati
ve E
xp
on
en
t P
rop
ert
yF
or
any n
onzero
num
ber
a a
nd a
ny inte
ger
n,
a -
n =
1 −
a n a
nd
1 −
a -
n =
a n .
Th
e s
imp
lifi
ed
form
of
an
exp
ress
ion
con
tain
ing n
egati
ve e
xp
on
en
ts m
ust
con
tain
on
ly
posi
tive e
xp
on
en
ts.
S
imp
lify
4 a
-3 b
6 −
16 a
2 b
6 c -
5 .
Assu
me t
ha
t n
o d
en
om
ina
tor e
qu
als
zero
.
4 a
-3 b 6 −
16 a
2 b 6 c -5
=
( 4 −
16 ) ( a
-3 −
a 2 ) (
b 6 −
b 6 ) (
1 −
c -5
) G
roup p
ow
ers
with t
he s
am
e b
ase.
=
1 −
4 (
a -
3-
2 )(
b 6-
6 )(
c 5 )
Quotient
of
Pow
ers
and N
egative E
xponent
Pro
pert
ies
=
1 −
4 a
-5 b 0 c 5
Sim
plif
y.
=
1 −
4 ( 1
−
a 5 ) (1
) c 5
Negative E
xponent
and Z
ero
Exponent
Pro
pert
ies
=
c 5 −
4 a
5
Sim
plif
y.
Th
e s
olu
tion
is
c 5 −
4 a
5 .
Exerc
ises
Sim
pli
fy e
ach
ex
pressio
n.
Assu
me t
ha
t n
o d
en
om
ina
tor e
qu
als
zero
.
1.
2 2 −
2 -
3 2
5 o
r 32
2.
m −
m -
4 m
5
3. p
-8 −
p 3
1 −
p 1
1
4. b
-4 −
b -
5 b
5. (-
x -
1 y) 0
−
4 w
-1 y 2 w
−
4 y 2
6. ( a
2 b 3 ) 2
−
(a b
) -2
a6b
8
7. x
4 y 0 −
x -
2
x6
8. (6
a -
1 b
) 2 −
( b 2 ) 4
36 −
a 2 b
6
9. (3
rt ) 2
u -
4 −
r -1
t 2 u
7 9
r 3 −
u 1
1
10.
m -
3 t -
5 −
( m 2 t 3
) -1
1 −
mt 2
11. ( 4
m 2 n
2 −
8 m
-1 " ) 0
1
12. ( -
2m
n 2 ) -
3 −
4 m
-6 n
4
- m
3 −
32
n 1
0
7-2 Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-2
Ch
ap
ter
7
13
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Div
idin
g M
on
om
ials
Sim
pli
fy e
ach
ex
pressio
n.
Assu
me t
ha
t n
o d
en
om
ina
tor e
qu
als
zero
.
1. 6
5 −
6 4 6
1 o
r 6
2. 9
12 −
9 8
94 o
r 6561
3. x
4 −
x 2 x
2
4. r
3 t 2
−
r 3 t 4
1
−
t 2
5.
m −
m 3
1 −
m 2
6. 9
d 7 −
3 d
6 3d
7. 1
2 n
5 −
36n
n 4 −
3
8. w
4 x 3 −
w 4 x
x2
9. a
3 b 5 −
ab 2
a2b
3
10. m
7 p
2 −
m 3 p
2 m
4
11. -
21 w
5 x 2 −
7 w
4 x 5
- 3
w −
x 3
12. 3
2 x 3 y 2 z 5 −
-8
xy z 2 -
4x
2yz
3
13. ( 4
p 7 −
7 r 2 ) 2
1
6 p
14 −
49
r 4
14. 4-
4
1 −
44 o
r
1 −
256
15. 8-
2
1 −
82 o
r 1
−
64
16. ( 5
−
3 ) -
2
9
−
25
17. (
9 −
11 ) -
1
1
1 −
9
18.
h 3 −
h -
6 h
9
19. k
0(k
4)(
k-
6)
1 −
k 2
20. k-
1(ℓ-
6)(
m3)
m
3 −
k " 6
21. f -
7 −
f 4
1 −
f 11
22. ( 1
6 p
5 w
2 −
2 p
3 w
3 ) 0
1
23. f -
5 g 4 −
h -
2
g 4 h
2 −
f 5
24. 1
5 x 6 y -
9 −
5xy -
11
3x
5y
2
25. -
15 t 0
u -
1 −
5 u
3
- 3
−
u 4
26. 4
8 x 6 y 7 z 5 −
-6x y 5 z 6 - 8
x 5 y 2 −
z
7-2
Answers (Lesson 7-2)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
14
Gle
ncoe A
lgeb
ra 1
Practi
ce
Div
idin
g M
on
om
ials
Sim
pli
fy e
ach
ex
pressio
n.
Assu
me t
ha
t n
o d
en
om
ina
tor e
qu
als
zero
.
1.
8 8
−
8 4 8
4 o
r 4096
2. a
4 b 6
−
ab 3
a3b
3
3. x
y 2
−
xy
y
4. m
5 n
p
−
m 4 p
mn
5.
5 c 2 d
3
−
-4 c 2 d
- 5
d 2
−
4
6. 8
y 7 z 6
−
4 y 6 z 5 2
yz
7.
( 4 f 3
g
−
3 h
6 ) 3
6
4 f 9
g 3
−
27
h 1
8
8.
( 6 w
5
−
7 p
6 r 3 ) 2
36
w 1
0
−
49
p 1
2 r 6
9. -
4 x 2
−
24 x 5
-
1
−
6 x 3
10. x
3(y
-5)(
x-
8)
1
−
x 5 y 5
11. p
(q-
2)(
r-3)
p
−
q 2 r 3
12. 12
-2
1
−
144
13. ( 3
−
7 ) -
2
4
9
−
9
14. ( 4
−
3 ) -
4
8
1
−
256
15.
22 r 3 s 2
−
11 r 2 s -
3 2
rs5
16. -
15 w
0 u
-1
−
5 u
3
-
3
−
u 4
17.
8 c 3 d
2 f 4
−
4 c -
1 d
2 f -
3 2c
4f 7
18. ( x
-3 y 5
−
4 -
3 ) 0
1
19.
6 f -
2 g 3 h
5
−
54 f -
2 g -
5 h
3
g 8 h
2
−
g
20. -
12 t -
1 u
5 x -
4
−
2 t -
3 u
x 5
-
6 t 2
u 4
−
x 9
21.
r 4
−
(3r )
3
r
−
27
22.
m -
2 n
-5
−
( m 4 n
3 ) -
1
m 2
−
n 2
23. (
j -1 k 3 ) -
4
−
j 3 k 3
j −
k 1
5
24. (2
a -
2 b ) -
3
−
5 a
2 b 4
a 4
−
40
b 7
25. ( q
-1 r 3
−
q r -
2 ) -
5
q
10
−
r 25
26. ( 7
c -
3 d
3
−
c 5 d
h -
4 ) -
1
c 8
−
7 d
2 h
4
27. ( 2
x 3 y 2 z
−
3 x 4 y z -
2 ) -
2
9
x 2
−
4 y 2 z 6
28. B
IOLO
GY
A
lab t
ech
nic
ian
dra
ws
a s
am
ple
of
blo
od
. A
cu
bic
mil
lim
ete
r of
the b
lood
co
nta
ins
22
3 w
hit
e b
lood
cell
s an
d 2
25 r
ed
blo
od
cell
s. W
hat
is t
he r
ati
o o
f w
hit
e b
lood
ce
lls
to r
ed
blo
od
cell
s?
29. C
OU
NTIN
G T
he n
um
ber
of
thre
e-l
ett
er
“word
s” t
hat
can
be f
orm
ed
wit
h t
he E
ngli
sh
alp
habet
is 2
63.
Th
e n
um
ber
of
five-l
ett
er
“word
s” t
hat
can
be f
orm
ed
is
26
5.
How
man
y
tim
es
more
fiv
e-l
ett
er
“word
s” c
an
be f
orm
ed
th
an
th
ree-l
ett
er
“word
s”?
676
7-2
1
−
484
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-2
Ch
ap
ter
7
15
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Div
idin
g M
on
om
ials
1. C
HEM
ISTR
Y T
he n
ucl
eu
s of
a c
ert
ain
ato
m i
s 10
-1
3 c
en
tim
ete
rs a
cross
. If
th
e
nu
cleu
s of
a d
iffe
ren
t ato
m i
s 10
-1
1
cen
tim
ete
rs a
cross
, h
ow
man
y t
imes
as
larg
e i
s it
as
the f
irst
ato
m?
2. SPA
CE
T
he M
oon
is
ap
pro
xim
ate
ly 2
54
kil
om
ete
rs a
way f
rom
Eart
h o
n a
vera
ge.
Th
e O
lym
pu
s M
on
s volc
an
o o
n M
ars
st
an
ds
25 k
ilom
ete
rs h
igh
. H
ow
man
y
Oly
mp
us
Mon
s volc
an
oes,
sta
cked
on
top
of
on
e a
noth
er,
wou
ld f
it b
etw
een
th
e
surf
ace
of
the E
art
h a
nd
th
e M
oon
?
25
3=
15,6
25
3. E-M
AIL
S
pam
(als
o k
now
n a
s ju
nk
e-m
ail
) co
nsi
sts
of
iden
tica
l m
ess
ages
sen
t to
th
ou
san
ds
of
e-m
ail
use
rs.
Peop
le
oft
en
obta
in a
nti
-sp
am
soft
ware
to f
ilte
r ou
t th
e j
un
k e
mess
ages
they
rece
ive.
Su
pp
ose
Yvon
ne’s
an
ti-s
pam
so
ftw
are
fil
tere
d o
ut
10
2 e
s, a
nd
sh
e
rece
ived
10
4 e
s la
st y
ear.
Wh
at
fract
ion
of
her
e-m
ail
s w
ere
fil
tere
d o
ut?
W
rite
you
r an
swer
as
a m
on
om
ial.
10
-2
4. M
ETR
IC M
EA
SU
REM
EN
T C
on
sid
er
a
du
st m
ite t
hat
measu
res
10
-3 m
illi
mete
rs
in l
en
gth
an
d a
cate
rpil
lar
that
measu
res
10 c
en
tim
ete
rs l
on
g.
How
man
y t
imes
as
lon
g a
s th
e m
ite i
s th
e c
ate
rpil
lar?
10
5=
100,0
00
5. C
OM
PU
TER
S In
1995,
stan
dard
cap
aci
ty
for
a p
ers
on
al
com
pu
ter
hard
dri
ve w
as
40 m
egabyte
s (M
B).
In
2010,
a s
tan
dard
h
ard
dri
ve c
ap
aci
ty w
as
500 g
igabyte
s (G
B o
r G
ig).
Refe
r to
th
e t
able
belo
w.
Mem
ory
Cap
acit
y A
pp
roxim
ate
Co
nvers
ion
s
8 b
its =
1 b
yte
10
3 b
yte
s =
1 k
ilobyte
10
3 k
ilobyte
s =
1 m
egabyte
(m
eg)
10
3 m
egabyte
s =
1 g
igabyte
(gig
)
10
3 g
igabyte
s =
1 t
era
byte
10
3 t
era
byte
s =
1 p
eta
byte
a.
Th
e n
ew
er
hard
dri
ves
have a
bou
t h
ow
man
y t
imes
the c
ap
aci
ty o
f th
e
1995 d
rives?
b.
Pre
dic
t th
e h
ard
dri
ve c
ap
aci
ty i
n t
he
year
2025 i
f th
is r
ate
of
gro
wth
co
nti
nu
es.
c.
On
e k
ilobyte
of
mem
ory
is
wh
at
fract
ion
of
on
e t
era
byte
?
7-2
100
12,5
00
6.2
5 p
eta
byte
s
1
−
10
9
= 1
0 -
9
Answers (Lesson 7-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
16
Gle
ncoe A
lgeb
ra 1
En
rich
men
t
Patt
ern
s w
ith
Po
wers
Use
you
r ca
lcu
lato
r, i
f n
ece
ssary
, to
com
ple
te e
ach
patt
ern
.
a.
21
0 =
b.
51
0 =
c.
41
0 =
29 =
5
9 =
4
9 =
28 =
5
8 =
4
8 =
27 =
5
7 =
4
7 =
26 =
5
6 =
4
6 =
25 =
5
5 =
4
5 =
24 =
5
4 =
4
4 =
23 =
5
3 =
4
3 =
22 =
5
2 =
4
2 =
21 =
5
1 =
4
1 =
Stu
dy
th
e p
att
ern
s f
or a
, b
, a
nd
c a
bo
ve.
Th
en
an
sw
er t
he q
uesti
on
s.
1. D
esc
ribe t
he p
att
ern
of
the e
xp
on
en
ts f
rom
th
e t
op
of
each
colu
mn
to t
he b
ott
om
.
Th
e e
xp
on
en
ts d
ecre
ase b
y o
ne f
rom
each
ro
w t
o t
he o
ne b
elo
w.
2. D
esc
ribe t
he p
att
e rn
of
the p
ow
ers
fro
m t
he t
op
of
the c
olu
mn
to t
he b
ott
om
. T
o g
et
each
po
wer,
div
ide t
he p
ow
er
on
th
e r
ow
ab
ove b
y t
he b
ase (
2,
5,
or
4).
3. W
hat
wou
ld y
ou
exp
ect
th
e f
oll
ow
ing p
ow
ers
to b
e?
20 1
5
0 1
4
0 1
4. R
efe
r to
Exerc
ise 3
. W
rite
a r
ule
. T
est
it
on
patt
ern
s th
at
you
obta
in u
sin
g 2
2,
25,
an
d 2
4
as
base
s.
Stu
dy
th
e p
att
ern
belo
w.
Th
en
an
sw
er t
he q
uesti
on
s.
03 =
0 0
2 =
0 0
1 =
0 0
0 =
?
0
-1 d
oes
not
exis
t. 0
-2 d
oes
not
exis
t. 0
-3 d
oes
not
exis
t.
5. W
hy d
o 0
-1,
0-
2,
an
d 0
-3 n
ot
exis
t?
Neg
ati
ve e
xp
on
en
ts a
re n
ot
defi
ned
un
less t
he b
ase i
s n
on
zero
.
6. B
ase
d u
pon
th
e p
att
ern
, ca
n y
ou
dete
rmin
e w
heth
er
00 e
xis
ts?
No
, sin
ce t
he p
att
ern
0n =
0 b
reaks d
ow
n f
or
n ⊂
1.
7. T
he s
ym
bol
00 i
s ca
lled
an
in
dete
rm
ina
te,
wh
ich
mean
s th
at
it h
as
no u
niq
ue v
alu
e.
Th
us
it d
oes
not
exis
t as
a u
niq
ue r
eal
nu
mber.
Wh
y d
o y
ou
th
ink
th
at
00 c
an
not
equ
al
1?
A
nsw
ers
will
vary
. O
ne a
nsw
er
is t
hat
if 0
0 =
1,
then
1 =
1 −
1 =
1 0 −
0 0 =
( 1 −
0 ) 0
,
w
hic
h i
s a
fals
e r
esu
lt,
sin
ce d
ivis
ion
by z
ero
is n
ot
allo
wed
. T
hu
s,
00
can
no
t eq
ual
1.
45
2
16
25
4
64
125
8
256
625
16
1024
3125
32
4096
15,6
25
64
16,3
84
78,1
25
128
65,5
36
390,6
25
256
262,1
44
1,9
53,1
25
512
1,0
48,5
76
9,7
65,6
25
7-2
1024
An
y n
on
zero
nu
mb
er
to t
he z
ero
po
wer
eq
uals
on
e.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-3
Ch
ap
ter
7
17
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Scie
nti
fic N
ota
tio
n
Scie
ntif
ic N
otatio
n
Very
larg
e a
nd
very
sm
all
nu
mbers
are
oft
en
best
rep
rese
nte
d
usi
ng a
meth
od
kn
ow
n a
s scie
nti
fic n
ota
tio
n.
Nu
mbers
wri
tten
in
sci
en
tifi
c n
ota
tion
tak
e
the f
orm
a ×
10n,
wh
ere
1 ≤
a <
10
an
d n
is
an
in
teger.
An
y n
um
ber
can
be w
ritt
en
in
sc
ien
tifi
c n
ota
tion
.
7-3
Ex
press 3
4,0
20,0
00,0
00 i
n
scie
nti
fic n
ota
tio
n.
Ste
p 1
M
ove t
he d
eci
mal
poin
t u
nti
l it
is
to t
he r
igh
t of
the f
irst
non
zero
dig
it.
Th
e
resu
lt i
s a r
eal
nu
mber a
. H
ere
, a
= 3
.402.
Ste
p 2
N
ote
th
e n
um
ber
of
pla
ces n
an
d
the d
irect
ion
th
at
you
moved
th
e d
eci
mal
poin
t. T
he d
eci
mal
poin
t m
oved
10 p
lace
s to
the l
eft
, so
n =
10.
Ste
p 3
B
eca
use
th
e d
eci
mal
moved
to t
he
left
, w
rite
th
e n
um
ber
as a
× 1
0n.
34,0
20,0
00,0
00 =
3.4
020000000 ×
10
10
Ste
p 4
Rem
ove t
he e
xtr
a z
ero
s. 3
.402 ×
10
10
E
xp
ress 4
.11 ×
10
-6 in
sta
nd
ard
no
tati
on
.
Ste
p 1
T
he e
xp
on
en
t is
–6,
so n
= –
6.
Ste
p 2
B
eca
use
n <
0, m
ove t
he d
eci
mal
poin
t 6 p
lace
s to
th
e l
eft
.
4.1
1 ×
10
-6 ⇒
.0
00
00
41
1
Ste
p 3
4.1
1 ×
10
-6 ⇒
0.0
00
00
41
1
Rew
rite
; in
sert
a 0
befo
re t
he d
ecim
al poin
t.
Exam
ple
1Exam
ple
2
Exerc
ises
Ex
press e
ach
nu
mb
er i
n s
cie
nti
fic n
ota
tio
n.
1. 5,1
00,0
00
2. 80,3
00,0
00,0
00
3. 14,2
50,0
00
5
.1 ×
10
6
8.0
3 ×
10
10
1.4
25 ×
10
7
4. 68,0
70,0
00,0
00,0
00
5. 14,0
00
6. 901,0
50,0
00,0
00
6
.807 ×
10
13
1.4
× 1
04
9.0
105 ×
10
11
7. 0.0
049
8. 0.0
00301
9. 0.0
000000519
4
.9 ×
10-
3
3.0
1 ×
10-
4
5.1
9 ×
10-
8
10. 0.0
00000185
11. 0.0
02002
12. 0.0
0000771
1
.85 ×
10-
7
2.0
02 ×
10-
3
7.7
1 ×
10-
6
Ex
press e
ach
nu
mb
er i
n s
tan
da
rd
fo
rm
.
13. 4.9
1 ×
10
4
14. 3.2
× 1
0-
5
15. 6.0
3 ×
10
8
4
9,1
00
0.0
00032
603,0
00,0
00
16. 2.0
01 ×
10
-6
15. 1.0
0024 ×
10
10
18. 5 ×
10
5
0
.000002001
10,0
02,4
00,0
00
500,0
00
19. 9.0
9 ×
10
-5
20. 3.5
× 1
0-
2
21. 1.7
087 ×
10
7
0
.0000909
0.0
35
17,0
87,0
00
Answers (Lesson 7-2 and Lesson 7-3)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
18
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (continued)
Scie
nti
fic N
ota
tio
n
7-3
Pro
du
cts
an
d Q
uo
tien
ts i
n S
cien
tifi
c N
ota
tio
n
You
can
use
sci
en
tifi
c n
ota
tion
to
sim
pli
fy m
ult
iply
ing a
nd
div
idin
g v
ery
larg
e a
nd
very
sm
all
nu
mbers
.
E
va
lua
te (
9.2
× 1
0-
3)
(4 ×
10
8).
Ex
press t
he r
esu
lt i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
(9.2
× 1
0-
3)(
4 ×
10
8)
Origin
al E
xpre
ssio
n
=
(9.2
× 4
)(10-
3 ×
10
8)
Com
muta
tive a
nd
Associa
tive P
ropert
ies
=
36.8
× 1
05
Pro
duct
of
Pow
ers
=
(3.6
8 ×
10
1) ×
10
5
36.8
= 3
.68 ×
10
=
3.6
8 ×
10
6
Pro
duct
of
Pow
ers
=
3,6
80,0
00
Sta
ndard
Form
E
va
lua
te ( 6
.9 ×
10
7 )
−
( 3 ×
10
5 )
.
Ex
press t
he r
esu
lt i
n b
oth
scie
nti
fic
no
tati
on
an
d s
tan
da
rd
fo
rm
.
( 2.7
6 × 10 7 ) −
( 6.9
× 10 5 ) = ( 2
.76 −
6.9
) ( 1
0 7
−
10 5 )
Pro
duct
rule
for
fractions
=
0.4
× 1
02
Quotient
of
Pow
ers
=
4.0
× 1
0-
1 ×
10
2
0.4
= 4
.0 ×
10-
1
=
4.0
× 1
01
Pro
duct
of
Pow
ers
=
40
S
tandard
form
Exam
ple
1Exam
ple
2
Exerc
ises
Ev
alu
ate
ea
ch
pro
du
ct.
Ex
press t
he r
esu
lts i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
1. (3
.4 ×
10
3)(
5 ×
10
4)
2. (2
.8 ×
10-
4)(
1.9
× 1
07)
1.7
× 1
08;
170,0
00,0
00
5.3
2 ×
10
3;
5320
3. (6
.7 ×
10-
7)(
3 ×
10
3)
4. (8
.1 ×
10
5)(
2.3
× 1
0-
3)
2.0
1 ×
10
-3;
0.0
0201
1.8
63 ×
10
3;
1863
5. (1
.2 ×
10-
11)(
6 × 106)
6. (5
.9 × 104)(
7 × 10-8)
7.2
× 1
0-
5;
0.0
00072
4.1
3 ×
10
-3;
0.0
0413
Ev
alu
ate
ea
ch
qu
oti
en
t. E
xp
ress t
he r
esu
lts i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
7. ( 4
.9 × 1 0 -3 ) −
( 2.5
× 1 0 -4 )
8. 5
.8 × 10 4 −
5 × 10 -
2
1
.96 ×
10
1;
19.6
1.1
6 ×
10
6;
1,1
60,0
00
9. ( 1
.6 × 1 0 5 ) −
( 4 × 1 0 -4 )
10.
8.6 × 1
0 6 −
1.6 × 1
0 -
3
4.0
× 1
08;
400,0
00,0
00
5.3
75 ×
10
9;
5,3
75,0
00,0
00
11. ( 4
.2 × 1 0 -2 ) −
( 6 × 1 0 -7 )
12. 8
.1 × 1
0 5 −
2.7 × 1
0 4
7 ×
10
4;
70,0
00
3 ×
10
1;
30
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-3
Ch
ap
ter
7
19
Gle
ncoe A
lgeb
ra 1
7-3
Sk
ills
Pra
ctic
e
Scie
nti
! c
No
tati
on
Ex
press e
ach
nu
mb
er i
n s
cie
nti
fic n
ota
tio
n.
1. 3,4
00,0
00,0
00
2. 0.0
00000312
3. 2,0
91,0
00
4. 980,2
00,0
00,0
00,0
00
5. 0.0
0000000008
6. 0.0
0142
Ex
press e
ach
nu
mb
er i
n s
tan
da
rd
fo
rm
.
7. 2.1
× 1
05
8. 8.0
23 ×
10-
7
9. 3.6
3 ×
10-
6
10. 7.1
5 ×
10
8
11. 1.8
6 ×
10-
4
12. 4.9
× 1
05
Ev
alu
ate
ea
ch
pro
du
ct.
Ex
press t
he r
esu
lts i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
13. (6
.1 ×
10
5)(
2 ×
10
5)
14. (4
.4 ×
10
6)(
1.6
× 1
0-
9)
15. (8
.8 ×
10
8)(
3.5
× 1
0-
13)
16. (1
.35 ×
10
8)(
7.2
× 1
0-
4)
17. (2
.2 ×
10-
12)(
8 ×
10
6)
18. (3
.4 ×
10-
5)(
5.4
× 1
0-
4)
Ev
alu
ate
ea
ch
qu
oti
en
t. E
xp
ress t
he r
esu
lts i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
19. (9
.2 × 1
0-
8) −
(2 × 1
0-
6)
20. (4
.8 × 1
04) −
(3 × 1
0-
5)
21. (1
.161 × 1
0-
9)
−
(4.3
× 1
0-
6)
22. ( 4
.625 × 1
0 10 ) −
( 1.2
5 × 1
0 4 )
23. (2
.376 × 1
0-
4)
−
(7.2
× 1
0-
8)
24. (8
.74 × 1
0-
3)
−
(1.9
× 1
05)
Answers (Lesson 7-3)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
20
Gle
ncoe A
lgeb
ra 1
7-3
Practi
ce
Scie
nti
fic N
ota
tio
n
Ex
press e
ach
nu
mb
er i
n s
cie
nti
fic n
ota
tio
n.
1. 1,9
00,0
00
2. 0.0
00704
1
.9 ×
10
6
7.0
4 ×
10
-4
3. 50,0
40,0
00,0
00
4. 0.0
000000661
5
.004 ×
10
10
6.6
1 ×
10
-8
Ex
press e
ach
nu
mb
er i
n s
tan
da
rd
fo
rm
.
5. 5.3
× 1
07
6. 1.0
9 ×
10
-4
5
3,0
00,0
00
0.0
00109
7. 9.1
3 ×
10
3
8. 7.9
02 ×
10
-6
9
130
0.0
00007902
Ev
alu
ate
ea
ch
pro
du
ct.
Ex
press t
he r
esu
lts i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
9. (4
.8 ×
10
4)(
6 ×
10
6)
10. (7
.5 ×
10
-5)(
3.2
× 1
07)
2
.88 ×
10
11;
288,0
00,0
00,0
00
2.4
× 1
03;
2400
11. (2
.06 ×
10
4)(
5.5
× 1
0-
9)
12. (8
.1 ×
10
-6)(
1.9
6 ×
10
11)
1
.133 ×
10
-4;
0.0
001133
1.5
876 ×
10
6;
1,5
87,6
00
13. (5
.29 ×
10
8)(
9.7
× 1
04)
14. (1
.45 ×
10
-6)(
7.2
× 1
0-
5)
5
.1313 ×
10
13;
51,3
13,0
00,0
00,0
00
1.0
44 ×
10
-1
0;
0.0
000000001044
Ev
alu
ate
ea
ch
qu
oti
en
t. E
xp
ress t
he r
esu
lts i
n b
oth
scie
nti
fic n
ota
tio
n a
nd
sta
nd
ard
fo
rm
.
15. (4
.2 ×
1 0 5 )
−
(3 ×
1 0 -
3 )
16. (1
.76 ×
1 0
-11 )
−
(2
.2 ×
1 0
-5 )
1
.4 ×
10
8;
140,0
00,0
00
8 ×
10
-7;
0.0
000008
17. (7
.05 ×
1 0
12 )
−
(9
.4 ×
1 0 7 )
18. (2
.04 ×
1 0
-4 )
−
(3
.4 ×
1 0
5 )
7
.5 ×
10
4;
75,0
00
6 ×
10
-1
0;
0.0
000000006
19. G
RA
VIT
ATIO
N I
ssac
New
ton
’s t
heo
ry o
f u
niv
ersa
l gra
vit
ati
on s
tate
s th
at
the
equ
ati
on
F =
G m
1m
2
−
r2
can
be
use
d t
o ca
lcu
late
th
e am
oun
t of
gra
vit
ati
onal
forc
e in
new
ton
s
bet
wee
n t
wo
poi
nt
mass
es m
1 a
nd
m2 s
epara
ted
by a
dis
tan
ce r
. G
is
a c
onst
an
t eq
ual
to 6
.67 ×
10
-1
1 N
m2 k
g–2.
Th
e m
ass
of
the
eart
h m
1 i
s eq
ual
to 5
.97 ×
10
24 k
g,
the
mass
of
the
moo
n m
2 i
s eq
ual
to 7
.36 ×
10
22 k
g,
an
d t
he
dis
tan
ce r
bet
wee
n t
he
two
is 3
84,0
00,0
00 m
.
a.
Exp
ress
th
e d
ista
nce
r i
n s
cien
tifi
c n
otati
on.
3.8
4 ×
10
8 m
b.
Com
pu
te t
he
am
oun
t of
gra
vit
ati
onal
forc
e bet
wee
n t
he
eart
h a
nd
th
e m
oon
. E
xp
ress
you
r an
swer
in
sci
enti
fic
not
ati
on.
1.9
9 ×
10
20 n
ew
ton
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-3
Ch
ap
ter
7
21
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Scie
nti
fic N
ota
tio
n
1. PLA
NETS
Nep
tun
e’s
mea
n d
ista
nce
fro
m
the
sun
is
4,5
00,0
00,0
00 k
ilom
eter
s.
Ura
nu
s’ m
ean
dis
tan
ce f
rom
th
e su
n i
s 2,8
70,0
00,0
00 k
ilom
eter
s. E
xp
ress
th
ese
dis
tan
ces
in s
cien
tifi
c n
otati
on.
Nep
tun
e:
4.5
× 1
09
km
; U
ran
us:
2.8
7 ×
10
9km
2. PA
TH
OLO
GY
Th
e co
mm
on c
old
is
cau
sed
by t
he
rhin
ovir
us,
wh
ich
co
mm
only
mea
sure
s 2 ×
10
-8 m
in
d
iam
eter
. T
he
E.
coli
bact
eriu
m,
wh
ich
ca
use
s fo
od p
oiso
nin
g,
com
mon
ly
mea
sure
s 3 ×
10
-6 m
in
len
gth
. E
xp
ress
th
ese
mea
sure
men
ts i
n s
tan
dard
for
m.
Rh
ino
vir
us:
0.0
0000002 m
; E
. co
li:
0.0
00003 m
3. C
OM
MER
CIA
LS
A 3
0-s
econ
d
com
mer
cial
air
ed d
uri
ng t
he
2007 S
up
er
Bow
l co
st $
2,6
00,0
00.
A 3
0-s
econ
d
com
mer
cial
air
ed d
uri
ng t
he
1967 S
up
er
Bow
l co
st $
40,0
00.
Exp
ress
th
ese
valu
es
in s
cien
tifi
c n
otati
on.
How
man
y t
imes
m
ore
exp
ensi
ve
was
it t
o air
an
ad
ver
tise
men
t d
uri
ng t
he
2007 S
up
er
Bow
l th
an
th
e 1967 S
up
er B
owl?
2007 S
up
er
Bo
wl:
$ 2
.6 ×
10
6;
1967 S
up
er
Bo
wl:
$ 4
.0 ×
10
4;
65 ×
10
1 o
r 65 t
imes
mo
re
exp
en
siv
e
4. A
VO
GA
DR
O’S
NU
MB
ER
Avog
ad
ro’s
n
um
ber
is
an
im
por
tan
t co
nce
pt
in
chem
istr
y.
It s
tate
s th
at
the
nu
mber
6.0
22 ×
10
23 i
s ap
pro
xim
ate
ly e
qu
al
to
the
nu
mber
of
mol
ecu
les
in 1
2 g
ram
s of
ca
rbon
12.
Use
Avog
ad
ro’s
nu
mber
to
det
erm
ine
the
nu
mber
of
mol
ecu
les
in
5 ×
10
-7 g
ram
s of
carb
on 1
2.
2.5
09 ×
10
16
mo
lecu
les
5. C
OA
L R
ESER
VES
Th
e ta
ble
bel
ow s
how
s th
e n
um
ber
of
kil
ogra
ms
of c
oal
sele
ct
cou
ntr
ies
had
in
pro
ven
res
erve
at
the
end
of
2006. Co
al
Reserv
es,
2006
Co
un
try
Co
al
(kg
)
United S
tate
s2.4
6 ×
10
14
Russia
1.5
7 ×
10
14
India
9.2
4 ×
10
13
Rom
ania
4.9
4 ×
10
11
So
urce:
British P
etr
ole
um
a.
Exp
ress
each
cou
ntr
y’s
coa
l re
serv
es
in s
tan
dard
for
m.
Un
ited
Sta
tes:
246,0
00,0
00,0
00,0
00 k
g;
Ru
ssia
: 157,0
00,0
00,0
00,0
00 k
g;
Ind
ia:
92,4
00,0
00,0
00,0
00 k
g;
Ro
man
ia:
494,0
00,0
00,0
00 k
g
b.
How
man
y t
imes
mor
e co
al
doe
s th
e U
nit
ed S
tate
s h
ave
than
Rom
an
ia?
4.9
8 ×
10
2 o
r 498 t
imes
c.
On
e k
ilog
ram
of
coal
has
an
en
ergy
den
sity
of
2.4
× 1
07 j
oule
s. W
hat
is t
he
tota
l en
ergy d
ensi
ty o
f th
e U
nit
ed
Sta
tes’
coa
l re
serv
e? E
xp
ress
you
r an
swer
in
sci
enti
fic
not
ati
on.
5.9
0 ×
10
21
jou
les
7-3
Answers (Lesson 7-3)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
22
Gle
ncoe A
lgeb
ra 1
En
gin
eerin
g n
ota
tio
n i
s a v
ari
ati
on o
n s
cien
tifi
c n
otati
on w
her
e n
um
ber
s are
exp
ress
ed
as
pow
ers
of 1
000 r
ath
er t
han
as
pow
ers
of 1
0.
En
gin
eeri
ng n
otati
on t
ak
es t
he
fam
ilia
r fo
rm
of a
× 1
0n,
bu
t n
is
rest
rict
ed t
o m
ult
iple
s of
th
ree
an
d 1
≤ |
a|
< 1
000.
On
e ad
van
tage
to e
ngin
eeri
ng n
otati
on i
s th
at
nu
mber
s ca
n b
e n
eatl
y e
xp
ress
ed u
sin
g S
I p
refi
xes
. T
hes
e p
refi
xes
are
typ
icall
y u
sed
for
sci
enti
fic
mea
sure
men
ts.
1000
n10
nS
I P
refi
xS
ym
bo
l
10005
1015
peta
P
10004
1012
tera
T
10003
109
giga
G
10002
106
mega
M
10001
103
kilo
k
1000-1
10-3
milli
m
1000-2
10-6
micro
µ
1000-3
10-9
nano
n
1000-4
10-12
pico
p
1000-5
10-15
femto
f
N
UC
LEA
R P
OW
ER
T
he o
utp
ut
of
a n
ucle
ar p
ow
er p
lan
t is
mea
su
red
to b
e 6
20,0
00,0
00 w
att
s.
Ex
press t
his
nu
mb
er i
n e
ng
ineerin
g n
ota
tio
n a
nd
usin
g
SI
prefi
xes.
To
exp
ress
a n
um
ber
in
en
gin
eeri
ng n
otati
on,
firs
t co
nver
t th
e n
um
ber
to
scie
nti
fic
not
ati
on.
Ste
p 1
620,0
00,0
00 ⇒
6.2
0000000
a = 6.20000000
Ste
p 2
T
he
dec
imal
poi
nt
mov
ed 8
pla
ces
to t
he
left
, so
n =
8.
Ste
p 3
620,0
00,0
00 =
6.2
0000000 × 1
08 =
6.2
× 1
08
Bec
au
se 8
is
not
a m
ult
iple
of
3,
we
nee
d t
o ro
un
d d
own
n t
o th
e n
ext
mu
ltip
le o
f 3.
Ste
p 4
6.2
× 1
08 =
(6.2
× 1
0-
2) × 1
08
6.2 = 620 × 10-2
Ste
p 5
=
620 ×
10
6
Product of Powers
Th
e ou
tpu
t of
th
e p
ower
pla
nt
is 6
20 ×
10
6 w
att
s. U
sin
g t
he
chart
abov
e, t
he
pre
fix f
or 1
06 i
s fo
un
d t
o be
meg
a,
or M
. T
he
outp
ut
of t
he
pow
er p
lan
t is
620 m
egaw
att
s, o
r 620M
W.
Exerc
ises
Ex
press e
ach
nu
mb
er i
n e
ng
ineerin
g n
ota
tio
n.
1. 40,0
00,0
00,0
00 4
0 ×
10
9
2. 180,0
00,0
00,0
00,0
00 1
80 ×
10
12
3. 0.0
0006 6
0 ×
10-
6
4. 0.0
0000000000039 390 ×
10-
15
Ex
press e
ach
mea
su
rem
en
t u
sin
g S
I p
refi
xes.
5. 0.0
0000000014 g
ram
6. 40,0
00,0
00,0
00 w
att
s
1
40 p
ico
gra
ms (
pg
) 4
0 g
igaw
att
s (
GW
)
7. 63,1
00,0
00,0
00,0
00 b
yte
s 8. 0.0
000002 m
eter
6
3.1
tera
byte
s (
TB
) 2
00 n
an
om
ete
rs (
nm
)
En
rich
men
t
En
gin
eeri
ng
No
tati
on
7-3 Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-4
Ch
ap
ter
7
23
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Po
lyn
om
ials
Deg
ree o
f a P
oly
no
mia
l A
po
lyn
om
ial
is a
mon
omia
l or
a s
um
of
mon
omia
ls.
A
bin
om
ial
is t
he
sum
of
two
mon
omia
ls,
an
d a
trin
om
ial
is t
he
sum
of
thre
e m
onom
ials
. P
olyn
omia
ls w
ith
mor
e th
an
th
ree
term
s h
ave
no
spec
ial
nam
e. T
he
deg
ree
of
a m
onom
ial
is t
he
sum
of
the
exp
onen
ts o
f all
its
vari
able
s. T
he
deg
ree o
f th
e p
oly
no
mia
l is
th
e sa
me
as
the
deg
ree
of t
he
mon
omia
l te
rm w
ith
th
e h
igh
est
deg
ree.
D
ete
rm
ine w
heth
er e
ach
ex
pressio
n i
s a
po
lyn
om
ial.
If
so
, id
en
tify
the p
oly
no
mia
l a
s a
monomial, binomial,
or trinomial.
Th
en
fin
d t
he d
eg
ree o
f th
e
po
lyn
om
ial.
Exp
ressio
nP
oly
no
mia
l?M
on
om
ial,
Bin
om
ial,
or
Tri
no
mia
l?
Deg
ree o
f th
e
Po
lyn
om
ial
3x - 7
xyz
Yes. 3x - 7
xyz = 3
x + (-7
xyz),
which is the sum of two monomials
binomial
3
-25
Yes. -25 is a real number.
monomial
0
7n3 + 3
n-4
No. 3 n -4 = 3 −
n 4 , which is not a
monomial
none of these
—
9x3 + 4
x + x + 4 + 2
x
Yes. The expression simplifies to
9x3 + 7
x + 4, which is the sum of
three monomials
trinomial
3
Exerc
ises
Dete
rm
ine w
heth
er e
ach
ex
pressio
n i
s a
po
lyn
om
ial.
If
so
, id
en
tify
th
e p
oly
no
mia
l
as a
monomial, binomial,
or trinomial.
1. 36 y
es;
mo
no
mia
l 2.
3 −
q 2 +
5 n
o
3. 7x -
x +
5 y
es;
bin
om
ial
4. 8g
2h
- 7
gh
+ 2
yes;
trin
om
ial
5.
1 −
4 y 2 +
5y -
8 n
o
6. 6
x +
x2 yes;
bin
om
ial
Fin
d t
he d
eg
ree o
f ea
ch
po
lyn
om
ial.
7. 4x
2y
3z
6
8. -
2a
bc
3
9. 15m
1
10. r +
5t
1
11. 22 0
12. 18x
2 +
4yz -
10y 2
13. x
4 -
6x
2 -
2x
3 -
10
4
14. 2x
3y
2 -
4xy
3 5
15. -
2r8
x4 +
7r2
x -
4r7
x6 13
16. 9x
2 +
yz8
9
17. 8
b +
bc5
6
18. 4
x4y -
8zx
2 +
2x
5 5
19. 4x
2 -
1 2
20. 9
abc +
bc -
n5 5
21. h
3m
+ 6
h4m
2 -
7 6
7-4 Exam
ple
Answers (Lesson 7-3 and Lesson 7-4)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
24
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Po
lyn
om
ials
Wri
te P
oly
no
mia
ls i
n S
tan
dard
Fo
rm
Th
e t
erm
s of
a p
oly
nom
ial
are
usu
all
y
arr
an
ged
so t
hat
the t
erm
s are
in
ord
er
from
gre
ate
st d
egre
e t
o l
east
degre
e.
Th
is i
s ca
lled
th
e s
tan
da
rd
fo
rm
of
a p
oly
no
mia
l.
W
rit
e -
4x
2 +
9x
4 -
2x i
n s
tan
da
rd
fo
rm
. Id
en
tify
th
e l
ea
din
g
co
eff
icie
nt.
Ste
p 1
: F
ind
th
e d
egre
e o
f each
term
.
P
oly
nom
ial:
-
4x
2 +
9x
4 -
2x
D
egre
e:
2
4
1
Ste
p 2
: W
rite
th
e t
erm
s in
desc
en
din
g o
rder:
9x
4 -
4x
2 -
2x.
T
he l
ead
ing c
oeff
icie
nt
is 9
.
Exerc
ises
Writ
e e
ach
po
lyn
om
ial
in s
tan
da
rd
fo
rm
. Id
en
tify
th
e l
ea
din
g c
oeff
icie
nt.
1. 5x +
x2 +
6
2. 6
x +
9 -
4x
2
3. x
4 +
x3+
x2
x
2 +
5x +
6;
1
- 4
x2
+ 6
x +
9;
-4
x
4 +
x3 +
x2;
1
4. 2x
3 -
x +
3x
7
5. 2
x +
x2 -
5
6. 2
0x -
10x
2 +
5x
3
3
x7 +
2x
3 -
7;
3
x
2 +
2x -
5;
1
5x
3 -
10
x2 +
20x;
5
7. x
3 +
x5 -
x2
8. x
4 +
4x
3 -
7x
5 +
1
9. -
3x
6 -
x5 +
2x
8
x
5 +
x3 -
x2;
1
-
7x
5 +
x4 +
4x
3 +
1;
-7
2x
8 -
3x
6 -
x5;
2
10. 2
x7 -
x8
11. 3
x +
5x
4 -
2 -
x2
12. -
2x
4 +
x -
4x
5 +
3
-
x8 +
2x
7;
-1
5x
4 -
x2 +
3x -
2;
5
-4
x5 -
2x
4 +
x +
3;
-4
13. 2 -
x1
2
14. 5
x4 -
12
x -
3x
6
15. 9
x9 -
9 +
3x
3 -
6x
6
-
x1
2 +
2;
-1
-3
x6 +
5x
5 -
12x;
-3
9x
9 -
6x
6 +
3x
3 -
9;
9
7-4 Exam
ple
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-4
Ch
ap
ter
7
25
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Po
lyn
om
ials
Dete
rm
ine w
heth
er e
ach
ex
pressio
n i
s a
po
lyn
om
ial.
If
so
, id
en
tify
th
e p
oly
no
mia
l
as a
monomial, binomial,
or trinomial.
1. 5
mt
+ t
2
2. 4
by +
2b -
by
y
es;
bin
om
ial
yes;
bin
om
ial
3.
-32
4. 3
x −
7
y
es;
mo
no
mia
l y
es;
mo
no
mia
l
5. 5
x2 -
3x-
4
6. 2
c2 +
8c +
9 -
3
n
o
yes;
trin
om
ial
Fin
d t
he d
eg
ree o
f ea
ch
po
lyn
om
ial.
7. 12 0
8. 3
r4 4
9. b
+ 6
1
10. 4
a3 -
2a
3
11. 5
abc -
2b
2 +
1 3
12. 8
x5y
4 -
2x
8 9
Writ
e e
ach
po
lyn
om
ial
in s
tan
da
rd
fo
rm
. Id
en
tify
th
e l
ea
din
g c
oeff
icie
nt.
13. 3
x +
1 +
2x
2
14. 5
x -
6 +
3x
2
2
x2 +
3x +
1;
3
3x
2 +
5x -
6;
3
15. 9
x2 +
2 +
x3 +
x
16. -
3 +
3x
3 -
x2 +
4x
x
3 +
9x
2 +
x +
2;
1
3x
3 -
x2 +
4x -
3;
3
17. x
2 +
3x
3 +
27
- x
18. 25 -
x3 +
x
3
x3 +
x2 -
x +
27;
3
-x
3 +
x +
25;
-1
19. x -
3x
2 +
4 +
5x
3
20. x
2 +
64
- x
+ 7
x3
5
x3 -
3x
2 +
x +
4;
5
7x
3 +
x2 -
x +
64;
7
21. 6
x3 - 7
x5 +
x -
2x
2 +
1
22. 4 -
x +
3x
3 - 2
x2
-
7x
5 +
6x
3 -
2x
2 +
x +
1;
-7
3x
3 -
2x
2 -
x +
4;
3
23. 13 - 4
x9 +
x3
24. 17
x5 -
5x
17 +
2
-
4x
9 +
x3 +
13;
-4
-5
x1
7 +
17x
5 +
2;
-5
7-4
Answers (Lesson 7-4)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
26
Gle
ncoe A
lgeb
ra 1
Practi
ce
Po
lyn
om
ials
Dete
rm
ine w
heth
er e
ach
ex
pressio
n i
s a
po
lyn
om
ial.
If
so
, id
en
tify
th
e p
oly
no
mia
l
as a
monomial, binomial,
or trinomial.
1. 7
a2b
+ 3
b2 -
a2b
2. 1
−
5 y
3 +
y 2 -
9
3. 6g
2h
3k
y
es;
bin
om
ial
yes;
trin
om
ial
yes;
mo
no
mia
l
Fin
d t
he d
eg
ree o
f ea
ch
po
lyn
om
ial.
4. x +
3x
4 -
21x
2 +
x3 4
5. 3
g2h
3 +
g3h
5
6. -
2x
2y +
3xy
3 +
x2 4
7. 5
n3m
- 2
m3 +
n2m
4 +
n2 6
8. a
3b
2c +
2a
5c +
b3c2
6
9. 10r2
t2 +
4rt
2 -
5r3
t2 5
Writ
e e
ach
po
lyn
om
ial
in s
tan
da
rd
fo
rm
. Id
en
tify
th
e l
ea
din
g c
oeff
icie
nt.
10. 8
x2 -
15
+ 5
x5
11. 10x -
7 +
x4 +
4x
3
5
x5 +
8x
2 -
15;
5
x
4 +
4x
3 +
10x -
7;
1
12. 13
x2 -
5 +
6x
3 -
x
13. 4x +
2x
5 -
6x
3 +
2
6
x3 +
13x
2 -
x -
5;
6
2x
5 -
6x
3 +
4x +
2;
2
GEO
METR
Y W
rit
e a
po
lyn
om
ial
to r
esp
ect
the a
rea
of
ea
ch
sh
ad
ed
reg
ion
.
14.
ab
b
ab
- b
2
15.
d
d
2 -
1
−
4 π
d 2
16. M
ON
EY
Wri
te a
pol
yn
omia
l to
rep
rese
nt
the
valu
e of
t t
en-d
olla
r bil
ls,
f fi
fty-d
olla
r
bil
ls,
an
d h
on
e-h
un
dre
d-d
olla
r bil
ls.
10
t +
50
f +
10
0h
17. G
RA
VIT
Y T
he
hei
gh
t abov
e th
e gro
un
d o
f a b
all
th
row
n u
p w
ith
a v
eloc
ity o
f 96 f
eet
per
se
con
d f
rom
a h
eigh
t of
6 f
eet
is 6
+ 9
6t -
16t2
fee
t, w
her
e t
is t
he
tim
e in
sec
ond
s.
Acc
ord
ing t
o th
is m
odel
, h
ow h
igh
is
the
ball
aft
er 7
sec
ond
s? E
xp
lain
.
-106 f
t; T
he h
eig
ht
is n
eg
ati
ve b
ecau
se t
he m
od
el
do
es n
ot
acco
un
t fo
r th
e b
all h
itti
ng
th
e g
rou
nd
wh
en
th
e h
eig
ht
is 0
feet.
7-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-4
Ch
ap
ter
7
27
Gle
ncoe A
lgeb
ra 1
1. PR
IMES
Mei
is
tryin
g t
o li
st a
s m
an
y
pri
me
nu
mber
s as
she
can
for
a
chall
enge
pro
ble
m f
or h
er m
ath
cla
ss.
Sh
e fi
nd
s th
at
the
pol
yn
omia
l ex
pre
ssio
n
n2-
n+
41 c
an
be
use
d t
o gen
erate
so
me,
bu
t n
ot a
ll,
pri
me
nu
mber
s. W
hat
is t
he
deg
ree
of M
ei’s
pol
yn
omia
l?
2. PH
ON
E C
ALLS
A l
ong-d
ista
nce
te
lep
hon
e co
mp
an
y c
harg
es a
$19.9
5
stan
dard
mon
thly
ser
vic
e fe
e p
lus
$0.0
5
per
min
ute
of
lon
g-d
ista
nce
use
. W
rite
a
pol
yn
omia
l to
exp
ress
th
e m
onth
ly c
ost
of
the
ph
one
pla
n i
f x m
inu
tes
of l
ong-
dis
tan
ce t
ime
are
use
d p
er m
onth
. W
hat
is t
he
deg
ree
of t
he
pol
yn
omia
l?
$0.0
5x
+ $
19.9
5;
1
3. C
OSTU
MES
Jack
’s m
oth
er i
s se
win
g t
he
cap
e of
his
cos
tum
e fo
r a c
hari
ty m
ask
ed
ball
. T
he
patt
ern
for
th
e ca
pe
(lyin
g f
lat)
is
sh
own
bel
ow.
Th
e ra
diu
s of
th
e n
eck
h
ole
is 6
in
ches
. W
hat
is t
he
are
a,
in
squ
are
fee
t, o
f th
e fi
nis
hed
cap
e?
27.5
ft2
3 f
t
Fab
ric
Neck h
ole
4. A
RC
HIT
EC
TU
RE
Gra
ph
ing t
he
pol
yn
omia
l fu
nct
ion
y=-
x2+
3 p
rod
uce
s an
acc
ura
te d
raw
ing o
f th
e sh
ap
e of
an
arc
hw
ay i
nsi
de
a h
isto
rica
l li
bra
ry,
wh
ere
x i
s th
e h
oriz
onta
l d
ista
nce
in
m
eter
s fr
om t
he
base
of
the
arc
h a
nd
y i
s th
e h
eigh
t of
th
e arc
h.
At
x=
0,
wh
at
is
the
hei
gh
t of
th
e arc
h?
5. D
RIV
ING
A t
ruck
an
d a
car
leave
an
in
ters
ecti
on.
Th
e tr
uck
tra
vel
s so
uth
, an
d
the
car
travel
s ea
st.
Wh
en t
he
tru
ck h
ad
gon
e 24 m
iles
, th
e d
ista
nce
bet
wee
n t
he
car
an
d t
ruck
was
fou
r m
iles
mor
e th
an
th
ree
tim
es t
he
dis
tan
ce t
ravel
ed b
y t
he
car
hea
din
g e
ast
.
24 miA C
x m
i
B
North
a.
Su
pp
ose
the
tru
ck s
top
s at
poi
nt
C
an
d t
he
car
stop
s at
poi
nt
B.
Wri
te a
p
olyn
omia
l in
sta
nd
ard
for
m t
o ex
pre
ss t
he
sum
of
the
dis
tan
ces
travel
ed b
y t
he
car
an
d t
he
tru
ck.
x
+24
b.
Wri
te a
sim
pli
fied
pol
yn
omia
l to
ex
pre
ss t
he
per
imet
er o
f tr
ian
gle
AB
C.
4x
+28 m
i
Wo
rd
Pro
ble
m P
racti
ce
Po
lyn
om
ials
7-4
23 m
Answers (Lesson 7-4)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
28
Gle
ncoe A
lgeb
ra 1
En
rich
men
t7-4
xy
-1 1
−
2
-2 3
−
8
-1
0
01
12
1 1
−
2
4 3
−
8
x
y
O
Po
lyn
om
ial
Fu
ncti
on
sS
up
pose
a l
inear
equ
ati
on
su
ch a
s -
3x +
y =
4
is
solv
ed
for
y.
Th
en
an
equ
ivale
nt
equ
ati
on
, y =
3x +
4,
is f
ou
nd
. E
xp
ress
ed
in
th
is w
ay,
y i
s a f
un
ctio
n o
f x,
or
f(x) =
3x +
4.
Noti
ce t
hat
the
righ
t si
de o
f th
e e
qu
ati
on
is
a b
inom
ial
of
degre
e 1
.
Hig
her-
degre
e p
oly
nom
ials
in
x m
ay a
lso f
orm
fu
nct
ion
s. A
n e
xam
ple
is
f(x) =
x3 +
1,
wh
ich
is
a p
oly
nom
ial
fun
ctio
n o
f d
egre
e 3
. Y
ou
can
gra
ph
th
is f
un
ctio
n u
sin
g a
table
of
ord
ere
d
pair
s, a
s sh
ow
n a
t th
e r
igh
t.
Fo
r e
ach
of
the f
oll
ow
ing
po
lyn
om
ial
fun
cti
on
s,
ma
ke a
ta
ble
of
va
lues f
or x
a
nd
y =
f(x
). T
hen
dra
w t
he g
ra
ph
on
th
e g
rid
.
1. f(
x) =
1 -
x2
2. f(
x) =
x2 -
5
xO
f(x)
xO
f(x)
3. f(
x) =
x2 +
4x - 1
4. f(
x) =
x3
xO
f(x)
xO
f(x)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-4
Ch
ap
ter
7
29
Gle
ncoe A
lgeb
ra 1
Gra
ph
ing C
alc
ula
tor
Act
ivit
y
Seco
nd
Deg
ree P
oly
no
mia
l Fu
ncti
on
s
Man
y r
eal
worl
d p
roble
ms
can
be m
od
ele
d u
sin
g p
oly
nom
ial
fun
ctio
ns.
Th
e T
AB
LE
fu
nct
ion
can
be u
sed
to e
valu
ate
a f
un
ctio
n f
or
mu
ltip
le v
alu
es.
Exerc
ises
1. A
n o
bje
ct i
s d
rop
ped
fro
m t
he t
op
of
a b
uil
din
g t
hat
is 4
12 f
eet
hig
h.
Th
e d
ista
nce
, in
fe
et,
above t
he g
rou
nd
at
x s
eco
nd
s is
giv
en
by P
(x) =
-16
x2 +
412.
a.
Aft
er
how
man
y s
eco
nd
s w
ill
the o
bje
ct b
e 1
00 f
eet
above t
he g
rou
nd
? ≈ 4
.4 s
b.
How
man
y s
eco
nd
s w
ill
it t
ak
e t
he o
bje
ct t
o r
each
th
e g
rou
nd
? ≈ 5
.1 s
2. A
bu
ngee j
um
per
free f
all
s fr
om
th
e R
oyal
Gorg
e s
usp
en
sion
bri
dge o
ver
the A
rkan
sas
Riv
er,
1053 f
eet
above t
he r
iver.
Th
e h
eig
ht
h o
f th
e b
un
gee j
um
per
above t
he r
iver,
in
fe
et,
aft
er
t se
con
ds
can
be r
ep
rese
nte
d b
y h
= -
16t2
+ 1
053. T
wo s
eco
nd
s aft
er
the f
irst
bu
ngee j
um
per
fall
s, a
noth
er
pers
on
ju
mp
s d
ow
n w
ith
an
in
itia
l velo
city
of
80 f
eet
per
seco
nd
. T
he p
osi
tion
of
the s
eco
nd
ju
mp
er
can
be r
ep
rese
nte
d b
y t
he e
qu
ati
on
h =
-16(t
- 2
)2 -
80(t
- 2
) +
1053.
a
. If
th
e b
un
gee c
ord
s are
desi
gn
ed
to s
tretc
h j
ust
en
ou
gh
so t
hat
the j
um
pers
tou
ch t
he
wate
r befo
re s
pri
ngin
g b
ack
up
, w
hic
h j
um
per
wil
l to
uch
th
e w
ate
r fi
rst?
How
lon
g
does
it t
ak
e e
ach
ju
mp
er
to t
ou
ch t
he w
ate
r? th
e s
eco
nd
ju
mp
er;
8.1
s,
6.0
s
b
. Does
the s
eco
nd
ju
mp
er
catc
h u
p t
o t
he f
irst
ju
mp
er?
If
so,
how
far
are
th
ey a
bove t
he
river
at
this
poin
t an
d h
ow
lon
g d
oes
it t
ak
e e
ach
ju
mp
er
to r
each
th
is p
oin
t?
yes;
477 f
t; 6
s,
4 s
A
n o
bje
ct
is d
ro
pp
ed
fro
m t
he t
op
of
a 1
79-f
oo
t cli
ff t
o
the w
ate
r b
elo
w. T
he h
eig
ht
of
the o
bje
ct
ab
ov
e t
he w
ate
r c
an
be m
od
ele
d b
y
h(t
) =
-16t2 + 1
79 w
here t
is t
ime i
n s
eco
nd
s.
a
. D
ete
rm
ine t
he h
eig
ht
of
the o
bje
ct
aft
er 0
.5 s
eco
nd
, 1 s
eco
nd
, 1.5
seco
nd
s,
an
d 2
seco
nd
s.
En
ter
the f
un
ctio
n i
nto
Y1
. U
se T
BL
SE
T t
o s
et
up
th
e
calc
ula
tor
to d
isp
lay v
alu
es
of
t in
0.5
seco
nd
in
terv
als
. D
isp
lay
the t
able
an
d r
eco
rd t
he r
esu
lts.
Exam
ine t
he t
able
. W
hen
x =
0.5
, y =
175.
Th
is m
ean
s th
at
h(0
.5) =
175, or
that
aft
er
0.5
seco
nd
, th
e o
bje
ct i
s 175 f
eet
above
the w
ate
r. T
hu
s, h
(1) =
163 f
eet,
h(1
.5) =
143 f
eet,
an
d
h(2
) =
115 f
eet.
b. A
fter h
ow
ma
ny
seco
nd
s d
oes t
he o
bje
ct
hit
th
e w
ate
r?
Ro
un
d t
o t
he n
ea
rest
hu
nd
red
th.
Scr
oll
th
rou
gh
th
e t
able
. N
oti
ce t
hat
the y
-valu
es
chan
ge f
rom
posi
tive t
o n
egati
ve b
etw
een
x =
3 a
nd
x =
3.5
. E
xam
ine t
his
inte
rval
more
clo
sely
by r
ese
ttin
g t
he t
able
usi
ng T
blS
tart=
3
an
d ∆
Tb
l= 0
.1.
Look
for
the c
han
ge i
n s
ign
.
Fu
rth
er
exam
ine t
he i
nte
rval
from
x =
3.3
to x
= 3
.4 u
sin
g
Tb
lSta
rt=
3.3
an
d ∆
Tb
l= 0
.01.
Th
e y
-valu
e c
lose
st t
o z
ero
occ
urs
wh
en
x =
3.3
4.
Th
us,
th
e
obje
ct h
its
the w
ate
r aft
er
abou
t 3.3
4 s
eco
nd
s.
7-4 Exam
ple
Answers (Lesson 7-4)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
30
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Ad
din
g a
nd
Su
btr
acti
ng
Po
lyn
om
ials
Ad
d P
oly
no
mia
ls
To a
dd
poly
nom
ials
, you
can
gro
up
lik
e t
erm
s h
ori
zon
tall
y o
r w
rite
th
em
in
colu
mn
form
, ali
gn
ing l
ike t
erm
s vert
icall
y.
Lik
e t
erm
s a
re m
on
om
ial
term
s th
at
are
eit
her
iden
tica
l or
dif
fer
on
ly i
n t
heir
coeff
icie
nts
, su
ch a
s 3p
an
d -
5p
or
2x
2y a
nd
8x
2y.
F
ind
(2x
2 +
x -
8) +
(3x
- 4x
2 +
2).
Ho
riz
on
tal
Meth
od
Gro
up
lik
e t
erm
s.
(2x
2 +
x -
8) +
(3
x -
4x
2 +
2)
=
[(2
x2 +
(-
4x
2)]
+ (
x +
3x) +
[(-
8) +
2)]
=
-2
x2 +
4x -
6.
Th
e s
um
is -
2x
2 +
4x -
6.
F
ind
(3x
2 +
5xy) +
(xy +
2x
2).
Verti
ca
l M
eth
od
Ali
gn
lik
e t
erm
s in
colu
mn
s an
d a
dd
.
3
x2 +
5xy
(+)
2x
2 +
xy
Put
the t
erm
s in d
escendin
g o
rder.
5
x2 +
6xy
Th
e s
um
is
5x
2 +
6xy.
Exerc
ises
Fin
d e
ach
su
m.
1. (4
a -
5) +
(3
a +
6)
2. (6
x +
9) +
(4
x2 -
7)
7
a +
1
4
x2 +
6x +
2
3. (6
xy +
2y +
6x) +
(4
xy -
x)
4. (x
2 +
y2) +
(-
x2 +
y2)
10
xy +
5x +
2y
2y
2
5. (3
p2 -
2p
+ 3
) +
(p
2 -
7p
+ 7
) 6. (2
x2 +
5xy +
4y
2) +
(-
xy -
6x
2 +
2y
2)
4
p2 -
9p
+ 1
0
-
4x
2 +
4xy +
6y
2
7. (5
p +
2q
) +
(2p
2 -
8q +
1)
8. (4
x2 -
x +
4) +
(5
x +
2x
2 +
2)
2
p2 +
5p
- 6
q +
1
6x
2 +
4x +
6
9. (6
x2 +
3x) +
(x
2 -
4x -
3)
10. (x
2 +
2xy +
y2) +
(x
2 -
xy -
2y
2)
7
x2 -
x -
3
2
x2 +
xy -
y2
11. (2
a -
4b -
c) +
(-
2a
- b
- 4
c)
12. (6
xy
2 +
4xy) +
(2xy -
10xy
2 +
y2)
-
5b
- 5
c
-
4xy
2 +
6xy +
y2
13. (2
p -
5r)
+ (
3p
+ 6
r) +
( p
- r
) 14. (2
x2 -
6) +
(5x
2 +
2) +
(-
x2 -
7)
6
p
6
x2 -
11
15. (3
z2 +
5z)
+ (
z2 +
2z)
+ (
z -
4)
16. (8
x2 +
4x +
3y
2 +
y) +
(6
x2 -
x +
4y)
4
z2
+ 8
z -
4
14x
2 +
3x +
3y
2 +
5y
7-5
Exam
ple
1Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-5
Ch
ap
ter
7
31
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Ad
din
g a
nd
Su
btr
acti
ng
Po
lyn
om
ials
Su
btr
act
Po
lyn
om
ials
Y
ou
can
su
btr
act
a p
oly
nom
ial
by a
dd
ing i
ts a
dd
itiv
e i
nvers
e.
To f
ind
th
e a
dd
itiv
e i
nvers
e o
f a p
oly
nom
ial,
rep
lace
each
term
wit
h i
ts a
dd
itiv
e i
nvers
e
or
op
posi
te.
F
ind
(3x
2 +
2x
- 6
) -
(2x
+ x
2 +
3).
Ho
riz
on
tal
Meth
od
Use
ad
dit
ive i
nvers
es
to r
ew
rite
as
ad
dit
ion
. T
hen
gro
up
lik
e t
erm
s.
(3x
2 +
2x -
6) -
(2x +
x2 +
3)
=
(3
x2 +
2x -
6) +
[(-
2x)+
(-
x2) +
(-
3)]
=
[3x
2 +
(-
x2)]
+ [
2x +
(-
2x)]
+ [-
6 +
(-
3)]
=
2x
2 +
(-
9)
=
2x
2 -
9
Th
e d
iffe
ren
ce i
s 2x
2 -
9.
Verti
ca
l M
eth
od
Ali
gn
lik
e t
erm
s in
colu
mn
s an
d
subtr
act
by a
dd
ing t
he a
dd
itiv
e i
nvers
e.
3x
2 +
2x -
6
(-)
x2 +
2x +
3
3
x2 +
2x -
6
(+) -
x2 -
2x -
3
2
x2
- 9
Th
e d
iffe
ren
ce i
s 2x
2 -
9.
Exerc
ises
Fin
d e
ach
dif
feren
ce.
1. (3
a -
5) -
(5a
+ 1
) 2. (9
x +
2) -
(-
3x
2 -
5)
-
2a -
6
3
x2 +
9x +
7
3. (9
xy +
y -
2x) -
(6
xy -
2x)
4. (x
2 +
y2) -
(-
x2 +
y2)
3
xy +
y
2x
2
5. (6
p2 +
4p
+ 5
) -
(2p
2 -
5p
+ 1
) 6. (6
x2 +
5xy -
2y
2) -
(-
xy -
2x
2 -
4y
2)
4
p2 +
9p
+ 4
8x
2 +
6xy +
2y
2
7. (8
p -
5r)
- (-
6p
2 +
6r -
3)
8. (8
x2 -
4x -
3) -
(-
2x -
x2 +
5)
6
p2 +
8p
- 1
1r +
3
9x
2 -
2x -
8
9. (3
x2 -
2x) -
(3x
2 +
5x -
1)
10. (4
x2 +
6xy +
2y
2) -
(-
x2 +
2xy -
5y
2)
-
7x +
1
5
x2
+ 4
xy +
7y
2
11. (2
h -
6j -
2k
) -
(-
7h
- 5
j -
4k
) 12. (9
xy
2 +
5xy) -
(-
2xy -
8xy
2)
9
h -
j +
2k
17xy
2 +
7xy
13. (2
a -
8b
) -
(-
3a
+ 5
b)
14. (2
x2 -
8) -
(-
2x
2 -
6)
5
a -
13b
4
x2 -
2
15. (6
z2 +
4z +
2) -
(4z2
+ z
) 16. (6
x2 -
5x +
1) -
(-
7x
2 -
2x +
4)
2
z2 +
3z +
2
13
x2 -
3x -
3
7-5 Exam
ple
Answers (Lesson 7-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
32
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Ad
din
g a
nd
Su
btr
acti
ng
Po
lyn
om
ials
Fin
d e
ach
su
m o
r d
ifferen
ce.
1. (2
x +
3y) +
(4x +
9y)
6x +
12y
2. (6
s +
5t)
+ (
4t +
8s)
14s +
9t
3. (5
a +
9b
) -
(2a
+ 4
b)
3a
+ 5
b
4. (1
1m
- 7
n) -
(2m
+ 6
n)
9m
- 1
3n
5. (m
2 -
m) +
(2m
+ m
2)
2m
2 +
m
6. (x
2 -
3x) -
(2x
2 +
5x) -
x2 -
8x
7. (d
2 -
d +
5) -
(2d
+ 5
) d
2 -
3d
8
. (2
h2 -
5h
) +
(7h
- 3
h2) -
h2 +
2h
9. (5
f +
g -
2) +
(-
2f +
3)
10. (6
k2 +
2k
+ 9
) +
(4k
2 -
5k
)
3f +
g +
1
10k
2 -
3k
+ 9
11. (x
3 -
x +
1) -
(3x -
1)
12. (b
2 +
ab -
2) -
(2b
2 +
2ab)
x
3 -
4x +
2
-
b2 -
ab
- 2
13. (7
z2 +
4 -
z) -
(-
5 +
3z2
) 14. (5
+ 4
n +
2t)
+ (-
6t -
8)
4
z2 -
z +
9
-
3 +
4n
- 4
t
15. (4
t2 +
2) +
(-
4 +
2t)
16. (3
g3 +
7g) -
(4g +
8g
3)
4
t2 +
2t -
2
-
5g
3 +
3g
17. (2
a2 +
8a
+ 4
) -
(a
2 -
3)
18. (3
x2 -
7x +
5) -
(-x
2 +
4x)
a
2 +
8a
+ 7
4
x2 -
11x +
5
19. (7
y2 +
y +
1) -
(-
4y +
3y
2 -
3)
20. (2
c2 +
7c +
4) +
(c2
+ 1
- 9
c)
4
y2 +
5y +
4
3
c2 -
2c
+ 5
21. (n
2 +
3n
+ 2
) -
(2n
2 -
6n
- 2
) 22. (a
2 +
ab
- 3
b2) +
(b
2 +
4a
2 -
ab
)
-
n2 +
9n
+ 4
5
a2 -
2b
2
23. (ℓ
2 -
5ℓ -
6) +
(2ℓ2
+ 5
+ ℓ
) 24. (2
m2 +
5m
+ 1
) -
(4m
2 -
3m
- 3
)
3ℓ
2 -
4ℓ -
1
-
2m
2 +
8m
+ 4
25. (x
2 -
6x +
2) -
(-
5x
2 +
7x -
4)
26. (5
b2 -
9b -
5) +
(b
2 -
6 +
2b
)
6x
2 -
13x +
6
6b
2 -
7b
- 1
1
27. (2
x2 -
6x -
2) +
(x
2 +
4x) +
(3x
2 +
x +
5)
6x
2 -
x +
3
7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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ME
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PE
RIO
D
Lesson 7 -5
Ch
ap
ter
7
33
Gle
ncoe A
lgeb
ra 1
Practi
ce
Adding and Subtracting Polynomials
Fin
d e
ach
su
m o
r d
ifferen
ce.
1. (4
y +
5) +
(-
7y -
1)
2. (-
x2 +
3x) -
(5x +
2x
2)
-
3y +
4
-
3x
2 -
2x
3. (4
k2 +
8k
+ 2
) -
(2k
+ 3
) 4. (2
m2 +
6m
) +
(m
2 -
5m
+ 7
)
4k
2 +
6k
- 1
3m
2 +
m +
7
5. (5
a2 +
6a
+ 2
) -
(7a
2 -
7a
+ 5
) 6. (-
4p
2 -
p +
9) +
( p
2 +
3p
- 1
)
-
2a
2 +
13a
- 3
-
3p
2 +
2p
+ 8
7. (x
3 -
3x +
1) -
(x
3 +
7 -
12x)
8. (6
x2 -
x +
1) -
(-
4 +
2x
2 +
8x)
9x -
6
4x
2 -
9x +
5
9. (4
y2 +
2y -
8) -
(7y
2 +
4 -
y)
10. (w
2 -
4w
- 1
) +
(-
5 +
5w
2 -
3w
)
-
3y
2 +
3y -
12
6w
2 -
7w
- 6
11. (4
u2 -
2u
- 3
) +
(3u
2 -
u +
4)
12. (5
b2 -
8 +
2b) -
(b
+ 9
b2 +
5)
7u
2 -
3u
+ 1
-
4b
2 +
b -
13
13. (4
d2 +
2d
+ 2
) +
(5d
2 -
2 -
d)
14. (8
x2 +
x -
6) -
(-x
2 +
2x -
3)
9d
2 +
d
9x
2 -
x -
3
15. (3
h2 +
7h
- 1
) -
(4h
+ 8
h2 +
1)
16. (4
m2 -
3m
+ 1
0) +
(m
2 +
m -
2)
-
5h
2 +
3h
- 2
5m
2 -
2m
+ 8
17. (x
2 +
y2 -
6) -
(5x
2 -
y2 -
5)
18. (7
t2 +
2 -
t) +
(t2
- 7
- 2
t)
-
4x
2 +
2y
2 -
1
8t2
- 3t -
5
19. (k
3 -
2k
2 +
4k +
6) -
(-
4k
+ k
2 -
3)
20. (9
j 2 +
j +
jk
) +
(-
3j 2
- jk -
4j)
k
3 -
3k
2 +
8k
+ 9
6j2
- 3j
21. (2
x +
6y -
3z)
+ (
4x +
6z -
8y) +
(x -
3y +
z)
7x -
5y +
4z
22. (6
f 2 -
7f -
3) -
(5f
2 -
1 +
2f)
- (
2f 2 -
3 +
f) -f 2
- 1
0f +
1
23. B
USIN
ESS
T
he p
oly
nom
ial s3
- 7
0s2
+ 1
500s -
10,8
00 m
od
els
th
e p
rofi
t a c
om
pan
y
mak
es
on
sell
ing a
n i
tem
at
a p
rice
s.
A s
eco
nd
ite
m s
old
at
the s
am
e p
rice
bri
ngs
in a
p
rofi
t of s3
- 3
0s2
+ 4
50s -
5000.
Wri
te a
poly
nom
ial
that
exp
ress
es
the t
ota
l p
rofi
t fr
om
the s
ale
of
both
ite
ms.
2s
3 -
10
0s
2 +
1950s -
15,8
00
24. G
EO
METR
Y T
he m
easu
res
of
two s
ides
of
a t
rian
gle
are
giv
en
. If
P i
s th
e p
eri
mete
r, a
nd
P =
10x +
5y,
fin
d t
he m
easu
re o
f
the t
hir
d s
ide.
2x +
2y
7-5
3x+
4y
5x-
y
Answers (Lesson 7-5)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
34
Gle
ncoe A
lgeb
ra 1
1. B
UIL
DIN
G F
ind
th
e s
imp
lest
exp
ress
ion
fo
r th
e p
eri
mete
r of
the t
rian
gu
lar
roof
tru
ss.
5a2
+ a
3a
+ 4
2a
- 7
2. G
EO
METR
Y W
rite
a p
oly
nom
ial
to s
how
th
e a
rea o
f th
e l
arg
e s
qu
are
belo
w.
a
2+
2ab+
b2
a
a
b
b
3. FIR
EW
OR
KS
T
wo b
ott
le r
ock
ets
are
la
un
ched
str
aig
ht
up
in
to t
he a
ir.
Th
e
heig
ht,
in
feet,
of
each
rock
et
at
t se
con
ds
aft
er
lau
nch
is
giv
en
by t
he p
oly
nom
ial
equ
ati
on
s belo
w.
Wri
te a
n e
qu
ati
on
to
show
how
mu
ch h
igh
er
Rock
et
A
travele
d.
Rock
et
A:
H1
=-
16t2
+ 1
22t
Rock
et
B:
H1
=-
16t2
+ 8
4t
D=
38t
4. EN
VELO
PES
A
n o
ffic
e s
up
ply
com
pan
y
pro
du
ces
yell
ow
docu
men
t en
velo
pes.
Th
e
en
velo
pes
com
e i
n a
vari
ety
of
sizes,
bu
t th
e l
en
gth
is
alw
ays
4 c
en
tim
ete
rs m
ore
th
an
dou
ble
th
e w
idth
. W
rite
a
poly
nom
ial
exp
ress
ion
to g
ive t
he
peri
mete
r of
an
y o
f th
e e
nvelo
pes.
6x+
8
5. IN
DU
STR
YT
wo i
den
tica
l ri
gh
t cy
lin
dri
cal
steel
dru
ms
con
tain
ing o
il
need
to b
e c
overe
d w
ith
a f
ire-r
esi
stan
t se
ala
nt.
In
ord
er
to d
ete
rmin
e h
ow
mu
ch
seala
nt
to p
urc
hase
, G
eorg
e m
ust
fin
d
the s
urf
ace
are
a o
f th
e t
wo d
rum
s. T
he
surf
ace
are
a (
incl
ud
ing t
he t
op
an
d
bott
om
base
s) i
s giv
en
by t
he f
oll
ow
ing
form
ula
.
S =
2π
rh
+ 2
πr
2
r h
a.
Wri
te a
poly
nom
ial
to r
ep
rese
nt
the
tota
l su
rface
are
a o
f th
e t
wo d
rum
s.
4π
rh+
4π
r2
b.
Fin
d t
he t
ota
l su
rface
are
a i
f th
e
heig
ht
of
each
dru
m i
s 2 m
ete
rs a
nd
th
e r
ad
ius
of
each
is
0.5
mete
rs.
Let
π=
3.1
4.
c.
Th
e f
ire r
esi
stan
t se
ala
nt
mu
st b
e
ap
pli
ed
wh
ile t
hey a
re s
tack
ed
vert
icall
y i
n g
rou
ps
of
thre
e.
If h
is
the h
eig
ht
of
each
dru
m a
nd
r i
s th
e
rad
ius,
wri
te a
poly
nom
ial
to
rep
rese
nt
the e
xp
ose
d s
urf
ace
are
a.
6π
rh+π
r2
Wo
rd
Pro
ble
m P
racti
ce
Ad
din
g a
nd
Su
btr
acti
ng
Po
lyn
om
ials
7-5
5a
2 +
6a
- 3
15.7
m2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-5
Ch
ap
ter
7
35
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Cir
cu
lar
Are
as a
nd
Vo
lum
es
A
rea
of
Cir
cle
V
olu
me o
f C
yli
nd
er
V
olu
me o
f C
on
e
A
= π
r2
V =
πr
2h
V
= 1
−
3 π
r 2 h
r
r
h
r
h
Writ
e a
n a
lgeb
ra
ic e
xp
ressio
n f
or e
ach
sh
ad
ed
area
. (R
eca
ll t
ha
t th
e d
iam
ete
r o
f a
cir
cle
is t
wic
e i
ts r
ad
ius.)
1.
x
x
2
.
yx
xy
3.
3x
2x
2x
x
π
x 2 -
π ( x
−
2 ) 2
= π
x 2
π
−
2 (
y 2 +
2xy)
1
9
−
2 π
x 2
Writ
e a
n a
lgeb
ra
ic e
xp
ressio
n f
or t
he t
ota
l v
olu
me o
f ea
ch
fig
ure.
4.
x
2x
5x
5.
3x
— 2
x+
a
x
x+
b
5
2 −
3 π
x 3
π
−
12 [13 x 3 +
(4a
+ 9
b) x
2 ]
Ea
ch
fig
ure h
as a
cy
lin
dric
al
ho
le w
ith
a r
ad
ius o
f 2 i
nch
es a
nd
a
heig
ht
of
5 i
nch
es.
Fin
d e
ach
vo
lum
e.
6.
5x
7x
7.
3x
4x
175
π
−
4
x3 -
20
π i
n 3
3
π x 3 -
20
π i
n 3
7-5
Answers (Lesson 7-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
36
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Mu
ltip
lyin
g a
Po
lyn
om
ial
by a
Mo
no
mia
l
Po
lyn
om
ial
Mu
ltip
lied
by M
on
om
ial
Th
e D
istr
ibu
tive P
rop
ert
y c
an
be u
sed
to
mu
ltip
ly a
poly
nom
ial
by a
mon
om
ial.
You
can
mu
ltip
ly h
ori
zon
tall
y o
r vert
icall
y.
Som
eti
mes
mu
ltip
lyin
g r
esu
lts
in l
ike t
erm
s. T
he p
rod
uct
s ca
n b
e s
imp
lifi
ed
by c
om
bin
ing l
ike t
erm
s.
F
ind
-3x
2(4x
2 +
6x -
8).
Ho
riz
on
tal
Meth
od
-3x
2(4
x2 +
6x -
8)
=
-3
x2(4
x2) +
(-
3x
2)(
6x) -
(-
3x
2)(
8)
=
-12x
4 +
(-
18
x3) -
(-
24x
2)
=
-12x
4 -
18x
3 +
24x
2
Verti
ca
l M
eth
od
4
x2 +
6x -
8
(×)
-3
x2
-
12x
4 -
18
x3 +
24x
2
Th
e p
rod
uct
is -
12x
4 -
18
x3 +
24
x2.
S
imp
lify
-2(4x
2 +
5x
) -
x(x
2 +
6x).
-2(4
x2 +
5x) -
x(
x2 +
6x)
=
-2(4
x2) +
(-
2)(
5x) +
(-
x)(
x2) +
(-
x)(
6x)
=
-8
x2 +
(-
10
x) +
(-
x3) +
(-
6x
2)
=
(-
x3) +
[-
8x
2 +
(-
6x
2)]
+ (-
10x)
=
-x
3 -
14x
2 -
10x
Exerc
ises
Fin
d e
ach
pro
du
ct.
1. x(5
x +
x2)
2. x(4
x2 +
3x +
2)
3. -
2xy(2
y +
4x
2)
5
x2 +
x3
4x
3+
3x
2+
2x
-
4xy
2 -
8x
3y
4. -
2g(g
2 -
2g +
2)
5. 3x(x
4 +
x3+
x2)
6. -
4x(2
x3 -
2x +
3)
-2
g3 +
4g
2 -
4g
3
x5 +
3x
4 +
3x
3
-
8x
4+
8x
2-
12x
7. -
4a
x(1
0 +
3x)
8. 3
y(-
4x -
6x
3-
2y)
9. 2x
2y
2(3
xy +
2y +
5x)
-40ax -
12ax
2
-
12xy -
18x
3y -
6y
2
6
x3y
3 +
4x
2y
3 +
10
x3y
2
Sim
pli
fy e
ach
ex
pressio
n.
10. x(3
x -
4) -
5x
11. -
x(2
x2 -
4x) -
6x
2
3
x2 -
9x
-
2x
3 -
2x
2
12. 6
a(2
a -
b) +
2a
(-4
a +
5b)
13. 4r(
2r2
- 3
r +
5) +
6r(
4r2
+ 2
r +
8)
4
a2 +
4ab
32r3
+ 6
8r
14. 4
n(3
n2 +
n -
4) -
n(3
- n
) 15. 2b
(b2 +
4b
+ 8
) -
3b(3
b2 +
9b
- 1
8)
12
n3 +
5n
2 -
19n
-7
b3 -
19b
2 +
70b
16. -
2z(
4z2
- 3
z +
1) -
z(3
z2 +
2z -
1)
17. 2(4
x2 -
2x) -
3(-
6x
2 +
4) +
2x(x
- 1
)
-11z
3 +
4z
2 -
z
28
x2 -
6x -
12
7-6
Exam
ple
1Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-6
Ch
ap
ter
7
37
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Mu
ltip
lyin
g a
Po
lyn
om
ial
by a
Mo
no
mia
l
So
lve E
qu
ati
on
s w
ith
Po
lyn
om
ial
Exp
ress
ion
s M
an
y e
qu
ati
on
s co
nta
in
poly
nom
ials
th
at
mu
st b
e a
dd
ed
, su
btr
act
ed
, or
mu
ltip
lied
befo
re t
he e
qu
ati
on
can
be s
olv
ed
.
S
olv
e 4
(n -
2)
+ 5n
= 6
(3 -
n)
+ 1
9.
4(n
- 2
) +
5n
= 6
(3 -
n) +
19
Origin
al equation
4n
- 8
+ 5
n =
18 -
6n
+ 1
9
Dis
trib
utive P
ropert
y
9n
- 8
= 3
7 -
6n
C
om
bin
e lik
e t
erm
s.
15n
- 8
= 3
7
Add 6
n t
o b
oth
sid
es.
15n
= 4
5
Add 8
to b
oth
sid
es.
n
= 3
D
ivid
e e
ach s
ide b
y 1
5.
Th
e s
olu
tion
is
3.
Exerc
ises
So
lve e
ach
eq
ua
tio
n.
1. 2(a
- 3
) =
3(-
2a
+ 6
) 3
2. 3(x
+ 5
) -
6 =
18
3
3. 3
x(x
- 5
) -
3x
2 =
-30 2
4. 6(x
2 +
2x) =
2(3
x2 +
12)
2
5. 4(2
p +
1) -
12
p =
2(8
p +
12)
-1
6. 2(6
x +
4) +
2 =
4(x
- 4
) -
3 1
−
4
7. -
2(4
y -
3) -
8y +
6 =
4(y
- 2
) 1
8. x(x
+ 2
) -
x(x
- 6
) =
10x -
12 6
9. 3(x
2 -
2x) =
3x
2 +
5x -
11 1
10. 2(4
x +
3) +
2 =
-4(x
+ 1
) -
1
11. 3(2
h -
6) -
(2h
+ 1
) =
9 7
12. 3(y
+ 5
) -
(4y -
8) =
-2y +
10
-13
13. 3(2
a -
6) -
(-
3a
- 1
) =
4a
- 2
3
14. 5(2
x2 -
1) -
(10
x2 -
6) =
-(x
+ 2
) -
3
15. 3(x
+ 2
) +
2(x
+ 1
) =
-5(x
- 3
)
7
−
10
16. 4(3
p2 +
2p
) -
12
p2 =
2(8
p +
6)
- 3
−
2
Exam
ple
7-6
Answers (Lesson 7-6)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
38
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Mu
ltip
lyin
g a
Po
lyn
om
ial
by a
Mo
no
mia
l
Fin
d e
ach
pro
du
ct.
1. a
(4a
+ 3
) 2.
-c(
11c
+ 4
)
4
a2 +
3a
-
11c
2 -
4c
3. x(2
x -
5)
4. 2
y( y
- 4
)
2
x2 -
5x
2y
2 -
8y
5.
-3n
(n2 +
2n
) 6. 4h
(3h
- 5
)
-
3n
3 -
6n
2
12
h2 -
20
h
7. 3x(5
x2 -
x +
4)
8. 7c(
5 -
2c2
+ c
3)
15
x3 -
3x
2 +
12x
35
c -
14
c3 +
7c
4
9.
-4b
(1 -
9b
- 2
b2)
10. 6
y(-
5 -
y +
4y
2)
-
4b
+ 3
6b
2 +
8b
3
-
30y -
6y
2 +
24y
3
11. 2m
2(2
m2 +
3m
- 5
) 12.
-3n
2(-
2n
2 +
3n
+ 4
)
4
m4 +
6m
3 -
10m
2
6
n4 -
9n
3 -
12n
2
Sim
pli
fy e
ach
ex
pressio
n.
13. w
(3w
+ 2
) +
5w
14. f (
5f
- 3
) -
2f
3
w2 +
7w
5
f 2 -
5f
15.
-p
(2p
- 8
) -
5p
16. y
2(-
4y +
5)
- 6
y2
-
2p
2 +
3p
-
4y
3 -
y2
17. 2x(3
x2 +
4)
- 3
x3
18. 4
a(5
a2 -
4)
+ 9
a
3
x3 +
8x
20
a3 -
7a
19. 4b
(-5b
- 3
) -
2(b
2 -
7b -
4)
20. 3m
(3m
+ 6
) -
3(m
2 +
4m
+ 1
)
-
22b
2 +
2b
+ 8
6
m2 +
6m
- 3
So
lve e
ach
eq
ua
tio
n.
21. 3(a
+ 2
) +
5 =
2a
+ 4
-7
22. 2(4
x +
2)
- 8
= 4
(x +
3)
4
23. 5( y
+ 1
) +
2 =
4( y
+ 2
) -
6 -
5
24. 4(b
+ 6
) =
2(b
+ 5
) +
2 -
6
25. 6(m
- 2
) +
14 =
3(m
+ 2
) -
10 -
2
26. 3(c
+ 5
) -
2 =
2(c
+ 6
) +
2 1
7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-6
Ch
ap
ter
7
39
Gle
ncoe A
lgeb
ra 1
Practi
ce
Mu
ltip
lyin
g a
Po
lyn
om
ial
by a
Mo
no
mia
l
Fin
d e
ach
pro
du
ct.
1. 2
h(-
7h
2 -
4h
) 2. 6
pq(3
p2 +
4q)
-
14
h3 -
8h
2
18
p3q
+ 2
4p
q2
3. 5
jk(3
jk +
2k
) 4.
-3rt
(-2t2
+ 3
r)
15
j2k
2 +
10
jk2
6rt
3 -
9r2
t
5.
- 1
−
4 m
(8 m
2 +
m -
7)
6.
- 2
−
3 n
2 (-
9 n
2 +
3n
+ 6
)
-
2 m
3 -
1 −
4 m
2 +
7 −
4 m
6
n4 -
2n
3 -
4n
2
Sim
pli
fy e
ach
ex
pressio
n.
7.
-2
"(3
" -
4)
+ 7
"
8. 5
w(-
7w
+ 3
) +
2w
(-2w
2 +
19
w +
2)
-
6"
2 +
15"
-
4w
3 +
3w
2 +
19w
9. 6
t(2t
- 3
) -
5(2
t2 +
9t
- 3
) 10.
-2(3
m3 +
5m
+ 6
) +
3m
(2m
2 +
3m
+ 1
)
2
t2 -
63t +
15
9m
2 -
7m
- 1
2
11.
-3
g(7
g -
2)
+ 3
( g
2 +
2g +
1)
- 3
g(-
5g +
3) -
3g
2 +
3g
+ 3
So
lve e
ach
eq
ua
tio
n.
12. 5(2
t -
1)
+ 3
= 3
(3t
+ 2
) 8
13. 3(3
u +
2)
+ 5
= 2
(2u
- 2
) -
3
14. 4(8
n +
3)
- 5
= 2
(6n
+ 8
) +
1
1 −
2
15. 8(3
b +
1)
= 4
(b +
3)
- 9
- 1
−
4
16. t(
t +
4)
- 1
= t
(t +
2)
+ 2
3
−
2
17. u
(u -
5)
+ 8
u =
u(u
+ 2
) -
4 -
4
18. N
UM
BER
TH
EO
RY
Let
x b
e an
in
teger
. W
hat
is t
he
pro
du
ct o
f tw
ice
the
inte
ger
ad
ded
to t
hre
e ti
mes
th
e n
ext
con
secu
tive
inte
ger
? 5
x +
3
19. IN
VESTM
EN
TS
K
ent
inves
ted
$5000 i
n a
ret
irem
ent
pla
n.
He
all
ocate
d x
dol
lars
of
the
mon
ey t
o a b
ond
acc
oun
t th
at
earn
s 4%
in
tere
st p
er y
ear
an
d t
he
rest
to
a t
rad
itio
nal
acc
oun
t th
at
earn
s 5%
in
tere
st p
er y
ear.
a
. W
rite
an
exp
ress
ion
th
at
rep
rese
nts
th
e am
oun
t of
mon
ey i
nves
ted
in
th
e tr
ad
itio
nal
acc
oun
t. 5
000 -
x
b
. W
rite
a p
olyn
omia
l m
odel
in
sim
ple
st f
orm
for
th
e to
tal
am
oun
t of
mon
ey T
Ken
t h
as
inves
ted
aft
er o
ne
yea
r. (
Hin
t: E
ach
acc
oun
t h
as
A +
IA
dol
lars
, w
her
e A
is
the
orig
inal
am
oun
t in
th
e acc
oun
t an
d I
is
its
inte
rest
rate
.) T
= 5
250 -
0.0
1x
c.
If K
ent
pu
t $500 i
n t
he
bon
d a
ccou
nt,
how
mu
ch m
oney
doe
s h
e h
ave
in h
is
reti
rem
ent
pla
n a
fter
on
e yea
r? $
5245
7-6
Answers (Lesson 7-6)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
40
Gle
ncoe A
lgeb
ra 1
Wo
rd
Pro
ble
m P
racti
ce
Mu
ltip
lyin
g a
Po
lyn
om
ial
by a
Mo
no
mia
l
1. N
UM
BER
TH
EO
RY
Th
e su
m o
f th
e fi
rst
n w
hol
e n
um
ber
s is
giv
en b
y t
he
exp
ress
ion
1 − 2
( n
2+
n).
Exp
an
d t
he
equ
ati
on b
y m
ult
iply
ing,
then
fin
d t
he
sum
of
the
firs
t 12 w
hol
e n
um
ber
s. n
2
− 2+
n − 2 ;
78
2. C
OLLEG
E T
roy’s
bos
s gave
him
$700 t
o st
art
his
col
lege
savin
gs
acc
oun
t. T
roy’s
bos
s als
o giv
es h
im $
40 e
ach
mon
th t
o ad
d t
o th
e acc
oun
t. T
roy’s
mot
her
giv
es
him
$50 e
ach
mon
th,
bu
t h
as
bee
n d
oin
g
so f
or 4
few
er m
onth
s th
an
Tro
y’s
bos
s.
Wri
te a
sim
pli
fied
exp
ress
ion
for
th
e am
oun
t of
mon
ey T
roy h
as
rece
ived
fro
m
his
bos
s an
d m
oth
er a
fter
m m
onth
s.
$90
m+
$500
3. LA
ND
MA
RK
S A
cir
cle
of 5
0 f
lags
surr
oun
ds
the
Wash
ingto
n M
onu
men
t.
Su
pp
ose
a n
ew s
idew
alk
12 f
eet
wid
e is
in
stall
ed j
ust
aro
un
d t
he
outs
ide
of t
he
circ
le o
f fl
ags.
Th
e ou
tsid
e ci
rcu
mfe
ren
ce
of t
he
sid
ewalk
is
1.1
0 t
imes
th
e ci
rcu
mfe
ren
ce o
f th
e ci
rcle
of
flags.
r
Cir
cle
of
flag
s
Sid
ewal
k
Wri
te a
n e
qu
ati
on t
hat
equ
ate
s th
e ou
tsid
e ci
rcu
mfe
ren
ce o
f th
e si
dew
alk
to
1.1
0 t
imes
th
e ci
rcu
mfe
ren
ce o
f th
e ci
rcle
of
fla
gs.
Sol
ve
the
equ
ati
on f
or t
he
rad
ius
of t
he
circ
le o
f fl
ags.
Rec
all
th
at
circ
um
fere
nce
of
a c
ircl
e is
2π
r.
1.1
0(2π
r) =
2π
(r+
12);
r=
120 f
t
4. M
AR
KET
Sop
hia
wen
t to
th
e fa
rmer
s’
mark
et t
o p
urc
hase
som
e veg
etable
s. S
he
bou
gh
t p
epp
ers
an
d p
otato
es.
Th
e p
epp
ers
wer
e $0.3
9 e
ach
an
d t
he
pot
ato
es w
ere
$0.2
9 e
ach
. S
he
spen
t $3.8
8 o
n v
eget
able
s, a
nd
bou
gh
t 4 m
ore
pot
ato
es t
han
pep
per
s. I
f x=
th
e n
um
ber
of
pep
per
s, w
rite
an
d s
olve
an
equ
ati
on
to f
ind
ou
t h
ow m
an
y o
f ea
ch v
eget
able
S
oph
ia b
ough
t.
$3.8
8 =
x(0
.39) +
(x+
4)(
0.2
9);
4 p
ep
pers
an
d 8
po
tato
es
5. G
EO
METR
YS
ome
mon
um
ents
are
co
nst
ruct
ed a
s re
ctan
gu
lar
pyra
mid
s.
Th
e vol
um
e of
a p
yra
mid
can
be
fou
nd
by
mu
ltip
lyin
g t
he
are
a o
f it
s base
B b
y o
ne
thir
d o
f it
s h
eigh
t. T
he
are
a o
f th
e re
ctan
gu
lar
base
of
a m
onu
men
t in
a
loca
l p
ark
is
giv
en b
y t
he
pol
yn
omia
l eq
uati
on B = x
2 - 4
x - 1
2.
h
a.
Wri
te a
pol
yn
omia
l eq
uati
on t
o re
pre
sen
t V
, th
e vol
um
e of
a
rect
an
gu
lar
pyra
mid
if
its
hei
gh
t is
10 c
enti
met
ers.
V=
10− 3
x 2-
40− 3
x-
40
b.
Fin
d t
he
vol
um
e of
th
e p
yra
mid
if
x=
12.
280 c
m3
7-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-6
Ch
ap
ter
7
41
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Fig
ura
te N
um
bers
Th
e n
um
ber
s bel
ow a
re c
all
ed p
en
tag
on
al
nu
mb
ers.
Th
ey a
re t
he
nu
mber
s of
dot
s or
d
isk
s th
at
can
be
arr
an
ged
as
pen
tagon
s.
22
12
51
1. F
ind
th
e p
rod
uct
1
−
2 n
(3n
- 1
).
3 n
2
−
2 -
n −
2
2. E
valu
ate
th
e p
rod
uct
in
Exer
cise
1 f
or v
alu
es o
f n
fro
m 1
th
rou
gh
4.
1,
5,
12,
22
3. W
hat
do
you
not
ice?
Th
ey a
re t
he f
irst
fou
r p
en
tag
on
al
nu
mb
ers
.
4. F
ind
th
e n
ext
six p
enta
gon
al
nu
mber
s. 3
5,
51,
70,
92,
117,
145
5. F
ind
th
e p
rod
uct
1
−
2 n
(n +
1).
n
2
−
2 +
n −
2
6. E
valu
ate
th
e p
rod
uct
in
Exer
cise
5 f
or v
alu
es o
f n
fro
m 1
th
rou
gh
5.
On
an
oth
er s
hee
t of
p
ap
er,
mak
e d
raw
ings
to s
how
wh
y t
hes
e n
um
ber
s are
call
ed t
he
tria
ngu
lar
nu
mber
s.
1,
3,
6,
10,
15
7. F
ind
th
e p
rod
uct
n(2
n -
1).
2n
2 -
n
8. E
valu
ate
th
e p
rod
uct
in
Exer
cise
7 f
or v
alu
es o
f n
fro
m 1
th
rou
gh
5.
Dra
w t
hes
e
hex
agon
al
nu
mber
s. 1
, 6,
15,
28,
45
9. F
ind
th
e fi
rst
5 s
qu
are
nu
mber
s. A
lso,
wri
te t
he
gen
eral
exp
ress
ion
for
an
y s
qu
are
nu
mber
. 1,
4,
9,
16,
25;
n2
Th
e n
um
ber
s you
have
exp
lore
d a
bov
e are
call
ed t
he
pla
ne
figu
rate
nu
mber
s bec
au
se t
hey
ca
n b
e arr
an
ged
to
mak
e geo
met
ric
figu
res.
You
can
als
o cr
eate
sol
id f
igu
rate
nu
mber
s.
10. If
you
pil
e 10 o
ran
ges
in
to a
pyra
mid
wit
h a
tri
an
gle
as
a b
ase
, you
get
on
e of
th
e te
trah
edra
l n
um
ber
s. H
ow m
an
y l
ayer
s are
th
ere
in t
he
pyra
mid
? H
ow m
an
y o
ran
ges
are
th
ere
in t
he
bot
tom
layer
s? 3
layers
; 6
11. E
valu
ate
th
e ex
pre
ssio
n
1 −
6 n
3 +
1 −
2 n
2 +
1 −
3 n
for
valu
es o
f n
fro
m 1
th
rou
gh
5 t
o fi
nd
th
e
firs
t fi
ve
tetr
ah
edra
l n
um
ber
s. 1,
4,
10,
20,
35
7-6
Answers (Lesson 7-6)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A20 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
42
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Mu
ltip
lyin
g P
oly
no
mia
ls
Mu
ltip
ly B
ino
mia
ls
To m
ult
iply
tw
o b
inom
ials
, you
can
ap
ply
th
e D
istr
ibu
tive
Pro
pert
y t
wic
e.
A u
sefu
l w
ay t
o k
eep
tra
ck o
f te
rms
in t
he p
rod
uct
is
to u
se t
he F
OIL
m
eth
od
as
illu
stra
ted
in
Exam
ple
2.
F
ind
(x +
3)(x -
4).
Ho
riz
on
tal
Meth
od
(x +
3)(
x -
4)
=
x(x
- 4
) +
3(x
- 4
)
=
(x)(
x) +
x(-
4) +
3(x
)+ 3
(-4)
=
x2 -
4x +
3x -
12
=
x2 -
x -
12
Verti
ca
l M
eth
od
x +
3
(×)
x -
4
-
4x -
12
x2 +
3x
x2 -
x -
12
Th
e p
rod
uct
is
x2 -
x -
12.
F
ind
(x
- 2
)(x +
5)
usin
g
the F
OIL
meth
od
.
(x -
2)(
x +
5)
F
irst
Oute
r In
ner
Last
=
(x)(
x) +
(x)(
5) +
(-
2)(
x) +
(-
2)(
5)
=
x2 +
5x +
(-
2x) -
10
=
x2 +
3x -
10
Th
e p
rod
uct
is
x2 +
3x -
10.
Exerc
ises
Fin
d e
ach
pro
du
ct.
1. (x
+ 2
)(x +
3)
2. (x
- 4
)(x +
1)
3. (x
- 6
)(x -
2)
x
2 +
5x +
6
x
2 -
3x -
4
x
2 -
8x +
12
4. ( p
- 4
)( p
+ 2
) 5
. ( y +
5)(
y +
2)
6. (2
x -
1)(
x +
5)
p
2 -
2p
- 8
y
2 +
7y +
10
2x
2 +
9x -
5
7. (3
n -
4)(
3n
- 4
) 8. (8
m -
2)(
8m
+ 2
) 9. (k
+ 4
)(5k
- 1
)
9
n2 -
24n
+ 1
6
64
m2 -
4
5
k2 +
19
k -
4
10. (3
x +
1)(
4x +
3)
11. (x
- 8
)(-
3x +
1)
12. (5
t +
4)(
2t -
6)
12
x2 +
13x +
3
-
3x
2 +
25x -
8
10
t2 -
22t -
24
13. (5
m -
3n
)(4m
- 2
n)
14. (a
- 3
b)(
2a
- 5
b)
15. (8
x -
5)(
8x +
5)
20
m2 -
22
mn
+ 6
n2
2
a2 -
11ab
+ 1
5b
2
64
x2 -
25
16. (2
n -
4)(
2n
+ 5
) 17. (4
m -
3)(
5m
- 5
) 18. (7
g -
4)(
7g +
4)
4
n2 +
2n
- 2
0
20
m2 -
35m
+ 1
5
49
g2 -
16
7-7
Exam
ple
1Exam
ple
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-7
Ch
ap
ter
7
43
Gle
ncoe A
lgeb
ra 1
Mu
ltip
ly P
oly
no
mia
ls
Th
e D
istr
ibu
tive P
rop
ert
y c
an
be u
sed
to m
ult
iply
an
y
two p
oly
nom
ials
.
F
ind
(3x
+ 2
)(2x
2 -
4x +
5).
(3x +
2)(
2x
2 -
4x +
5)
=
3x(2
x2 -
4x +
5) +
2(2
x2 -
4x +
5)
Dis
trib
utive P
ropert
y
=
6x
3 -
12
x2 +
15
x +
4x
2 -
8x +
10
D
istr
ibutive P
ropert
y
=
6x
3 -
8x
2 +
7x +
10
C
om
bin
e lik
e t
erm
s.
Th
e p
rod
uct
is
6x
3 -
8x
2 +
7x +
10.
Exerc
ises
Fin
d e
ach
pro
du
ct.
1. (x
+ 2
)(x
2 -
2x +
1)
2. (x
+ 3
)(2x
2 +
x -
3)
x
3 -
3x +
2
2
x3 +
7x
2 -
9
3. (2
x -
1)(
x2 -
x +
2)
4. (p
- 3
)(p
2 -
4p
+ 2
)
2
x3 -
3x
2 +
5x -
2
p
3 -
7p
2 +
14
p -
6
5. (3
k +
2)(
k2 +
k -
4)
6. (2
t +
1)(
10
t2 -
2t -
4)
3
k3 +
5k
2 -
10
k -
8
20t3
+ 6
t2 -
10
t -
4
7. (3
n -
4)(
n2 +
5n
- 4
) 8. (8
x -
2)(
3x
2 +
2x -
1)
3
n3 +
11
n2 -
32
n +
16
24
x3 +
10x
2 -
12x +
2
9. (2
a +
4)(
2a
2 -
8a
+ 3
) 10. (3
x -
4)(
2x
2 +
3x +
3)
4
a3 -
8a
2 -
26
a +
12
6x
3 +
x2 -
3x -
12
11. (n
2 +
2n
- 1
)(n
2 +
n +
2)
12. (t
2 +
4t -
1)(
2t2
- t
- 3
)
n
4 +
3n
3 +
3n
2 +
3n
- 2
2
t4 +
7t3
- 9
t2 -
11t +
3
13. (y
2 -
5y +
3)(
2y
2 +
7y -
4)
14. (3
b2 -
2b
+ 1
)(2b
2 -
3b -
4)
2
y4 -
3y
3 -
33y
2 +
41y -
12
6
b4 -
13
b3 -
4b
2 +
5b
- 4
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Mu
ltip
lyin
g P
oly
no
mia
ls
7-7 Exam
ple
Answers (Lesson 7-7)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A21 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
44
Gle
ncoe A
lgeb
ra 1
Sk
ills
Practi
ce
Mu
ltip
lyin
g P
oly
no
mia
ls
Fin
d e
ach
pro
du
ct.
1. (m
+ 4
)(m
+ 1
) 2. (x
+ 2
)(x +
2)
m
2 +
5m
+ 4
x
2 +
4x +
4
3. (b
+ 3
)(b
+ 4
) 4. (t
+ 4
)(t -
3)
b
2 +
7b
+ 1
2
t2
+ t
- 1
2
5. (r
+ 1
)(r -
2)
6. (n
- 5
)(n
+ 1
)
r2
- r
- 2
n
2 -
4n
- 5
7. (3
c +
1)(c -
2)
8. (2
x -
6)(x +
3)
3
c2 -
5c
- 2
2
x2 -
18
9. (d
- 1
)(5d
- 4
) 10. (2
ℓ +
5)(ℓ -
4)
5
d2 -
9d
+ 4
2ℓ
2 -
3ℓ -
20
11. (3
n -
7)(n
+ 3
) 12. (q
+ 5
)(5q
- 1
)
3
n2 +
2n
- 2
1
5q
2 +
24q
- 5
13. (3
b +
3)(
3b -
2)
14. (2
m +
2)(
3m
- 3
)
9
b2 +
3b
- 6
6
m2 -
6
15. (4
c +
1)(
2c +
1)
16. (5
a -
2)(
2a
- 3
)
8
c2 +
6c
+ 1
1
0a
2 -
19
a +
6
17. (4
h -
2)(
4h
- 1
) 18. (x
- y
)(2x -
y)
16
h2 -
12h
+ 2
2
x2 -
3xy +
y2
19. (w
+ 4
)(w
2 +
3w
- 6
) 20. (t
+ 1
)(t2
+ 2
t +
4)
w
3 +
7w
2 +
6w
- 2
4
t3
+ 3
t2 +
6t +
4
21. (k
+ 4
)(k
2 +
3k -
6)
22. (m
+ 3
)(m
2 +
3m
+ 5
)
k
3 +
7k
2 +
6k -
24
m
3 +
6m
2 +
14m
+ 1
5
7-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-7
Ch
ap
ter
7
45
Gle
ncoe A
lgeb
ra 1
Practi
ce
Mu
ltip
lyin
g P
oly
no
mia
ls
Fin
d e
ach
pro
du
ct.
1. (q
+ 6
)(q +
5)
2. (x
+ 7
)(x +
4)
q
2 +
11
q +
30
x
2 +
11x +
28
3. (n
- 4
)(n
- 6
) 4. (a
+ 5
)(a
- 6
)
n
2 -
10
n +
24
a
2 -
a -
30
5. (4
b +
6)(b
- 4
) 6. (2
x -
9)(
2x +
4)
4
b2 -
10
b -
24
4
x2 -
10x -
36
7. (6
a -
3)(
7a
- 4
) 8
. (2
x -
2)(
5x -
4)
4
2a
2 -
45a
+ 1
2
10
x2 -
18x +
8
9. (3
a -
b)(
2a
- b
) 10. (4
g +
3h
)(2g +
3h
)
6
a2 -
5ab
+ b
2
8g
2 +
18
gh
+ 9
h2
11. (m
+ 5
)(m
2 +
4m
- 8
) 12. (t
+ 3
)(t2
+ 4
t +
7)
m
3 +
9m
2 +
12
m -
40
t3
+ 7
t2 +
19t +
21
13. (2
h +
3)(
2h
2 +
3h
+ 4
) 14. (3
d +
3)(
2d
2 +
5d
- 2
)
4
h3 +
12
h2 +
17
h +
12
6
d3 +
21
d2 +
9d
- 6
15. (3
q +
2)(
9q
2 -
12q
+ 4
) 16. (3
r +
2)(
9r2
+ 6
r +
4)
27
q3 -
18q
2 -
12q
+ 8
27
r3 +
36r2
+ 2
4r +
8
17. (3
n2 +
2n
- 1
)(2n
2 +
n +
9)
18. (2
t2 +
t +
3)(
4t2
+ 2
t -
2)
6
n4 +
7n
3 +
27
n2 +
17n
- 9
8
t4 +
8t3
+ 1
0t2
+ 4
t -
6
19. (2
x2 -
2x -
3)(
2x
2 -
4x +
3)
20. (3
y2 +
2y +
2)(
3y
2 -
4y -
5)
4
x4 -
12x
3 +
8x
2 +
6x -
9
9
y4 -
6y
3 -
17y
2 -
18
y -
10
GEO
METR
Y W
rit
e a
n e
xp
ressio
n t
o r
ep
resen
t th
e a
rea
of
ea
ch
fig
ure.
21.
4x+
2
2x-
2
22.
3x+
2
5x-
4
23. N
UM
BER
TH
EO
RY
L
et x b
e a
n e
ven
in
teger.
Wh
at
is t
he p
rod
uct
of
the n
ext
two
con
secu
tive e
ven
in
tegers
?
24. G
EO
METR
Y T
he v
olu
me o
f a r
ect
an
gu
lar
pyra
mid
is
on
e t
hir
d t
he p
rod
uct
of
the a
rea o
f it
s base
an
d i
ts h
eig
ht.
Fin
d a
n e
xp
ress
ion
for
the v
olu
me o
f a r
ect
an
gu
lar
pyra
mid
w
hose
base
has
an
are
a o
f 3x
2 +
12x +
9 s
qu
are
feet
an
d w
hose
heig
ht
is x
+ 3
feet.
x
3 +
7x
2 +
15x +
9 f
t3
7-7
4x
2 -
2x -
2 u
nit
s2
4x
2 +
3x -
1 u
nit
s2
x2 +
6x +
8
Answers (Lesson 7-7)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A22 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
46
Gle
ncoe A
lgeb
ra 1
1. TH
EA
TER
T
he L
oft
Th
eate
r h
as
a c
en
ter
seati
ng s
ect
ion
wit
h 3
c+
8 r
ow
s an
d
4c
– 1
seats
in
each
row
. W
rite
an
exp
ress
ion
for
the t
ota
l n
um
ber
of
seats
in
th
e c
en
ter
sect
ion
.
2. C
RA
FTS
S
up
pose
a q
uil
t m
ad
e u
p o
f sq
uare
s h
as
a l
en
gth
-to-w
idth
rati
o o
f 5
to 4
. T
he l
en
gth
of
the q
uil
t is
5x i
nch
es.
T
he q
uil
t ca
n b
e m
ad
e s
ligh
tly l
arg
er
by
ad
din
g a
bord
er
of
1-i
nch
squ
are
s all
th
e
way a
rou
nd
th
e p
eri
mete
r of
the q
uil
t.
Wri
te a
poly
nom
ial
exp
ress
ion
for
the
are
a o
f th
e l
arg
er
qu
ilt.
20
x2+
18x+
4
3. SER
VIC
E A
fold
ed
Un
ited
Sta
tes
flag i
s so
meti
mes
pre
sen
ted
to i
nd
ivid
uals
in
re
cogn
itio
n o
f ou
tsta
nd
ing s
erv
ice t
o t
he
cou
ntr
y.
Th
e f
lag i
s p
rese
nte
d f
old
ed
in
a
tria
ngle
. O
ften
th
e r
eci
pie
nt
pu
rch
ase
s a
case
desi
gn
ed
to d
isp
lay t
he f
old
ed
fla
g t
o
pro
tect
it
from
wear.
On
e s
uch
dis
pla
y
case
has
dim
en
sion
s (i
n i
nch
es)
sh
ow
n
belo
w.
Wri
te a
poly
nom
ial
exp
ress
ion
th
at
rep
rese
nts
th
e a
rea o
f w
all
sp
ace
co
vere
d b
y t
he d
isp
lay c
ase
.
x 2 − 2
+
5 −
4 x
- 2
5 −
4
x+
5
x-
—5 2
So
urce:
Am
erica
n F
lag
Sto
re
4. M
ATH
FU
N T
hin
k o
f a w
hole
nu
mber.
S
ubtr
act
2.
Wri
te d
ow
n t
his
nu
mber.
T
ak
e t
he o
rigin
al
nu
mber
an
d a
dd
2.
Wri
te d
ow
n t
his
nu
mber.
Fin
d t
he
pro
du
ct o
f th
e n
um
bers
you
wro
te d
ow
n.
Su
btr
act
th
e s
qu
are
of
the o
rigin
al
nu
mber.
Th
e r
esu
lt i
s alw
ays
–4.
Use
p
oly
nom
ials
to s
how
how
th
is n
um
ber
tric
k w
ork
s.
(x-
2)(
x+
2) -
x2=-
4
x2-
2x+
2x-
4 -
x2=-
4
-4 =-
4
5. A
RT
Th
e m
use
um
wh
ere
Ju
lia w
ork
s p
lan
s to
have a
larg
e w
all
mu
ral
rep
lica
of
Vin
cen
t van
Gogh
’s T
he
Sta
rry N
igh
t
pain
ted
in
its
lobby.
Fir
st,
Ju
lia w
an
ts t
o
pain
t a l
arg
e f
ram
e a
rou
nd
wh
ere
th
e
mu
ral
wil
l be.
Th
e m
ura
l’s
len
gth
wil
l be
5 f
eet
lon
ger
than
its
wid
th,
an
d t
he
fram
e w
ill
be 2
feet
wid
e o
n a
ll s
ides.
Ju
lia h
as
on
ly e
nou
gh
pain
t to
cover
100
squ
are
feet
of
wall
su
rface
. H
ow
larg
e
can
th
e m
ura
l be?
Pain
ted
fra
me
Mu
ral
a.
Wri
te a
n e
xp
ress
ion
for
the a
rea o
f th
e m
ura
l.
b.
Wri
te a
n e
xp
ress
ion
for
the a
rea o
f th
e f
ram
e.
(w+
9)(
w+
4) -
(w+
5)w
c.
Wri
te a
nd
solv
e a
n e
qu
ati
on
to f
ind
h
ow
larg
e t
he m
ura
l ca
n b
e.
(w+
9)(
w+
4) -
(w+
5)w=
100
8 f
t b
y 1
3 f
t
Wo
rd
Pro
ble
m P
racti
ce
Mu
ltip
lyin
g P
oly
no
mia
ls
7-7
12c
2 +
29
c -
8
w(w
+ 5
)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7 -7
Ch
ap
ter
7
47
Gle
ncoe A
lgeb
ra 1
En
ric
hm
en
t
Pascal’s T
rian
gle
Th
is a
rra
ng
em
en
t o
f n
um
bers i
s c
all
ed
Pa
sca
l’s T
ria
ng
le.
It w
as f
irst
pu
bli
sh
ed
in
1665,
bu
t w
as k
no
wn
hu
nd
red
s
of
yea
rs e
arli
er.
1. E
ach
nu
mber
in t
he t
rian
gle
is
fou
nd
by a
dd
ing t
wo n
um
bers
. W
hat
two n
um
bers
were
ad
ded
to g
et
the 6
in
th
e 5
th r
ow
?
3
an
d 3
2. D
esc
ribe h
ow
to c
reate
th
e 6
th r
ow
of
Pasc
al’s
Tri
an
gle
.
T
he f
irst
an
d l
ast
nu
mb
ers
are
1.
Evalu
ate
1 +
4,
4 +
6,
6 +
4,
an
d 4
+ 1
to
fin
d t
he o
ther
nu
mb
ers
.
3. W
rite
th
e n
um
bers
for
row
s 6 t
hro
ugh
10 o
f th
e t
rian
gle
.
Row
6:
1 5 10 10 5 1
Row
7:
1 6 15 20 15 6 1
Row
8:
1 7 21 35 35 21 7 1
Row
9:
1 8 28 56 70 56 28 8 1
Row
10:
1 9 36 84 126 126 84 36 9 1
Mu
ltip
ly t
o f
ind
th
e e
xp
an
ded
fo
rm
of
ea
ch
pro
du
ct.
4. (a
+ b
)2 a
2 +
2ab
+ b
2
5. (a
+ b
)3 a
3 +
3a
2b
+ 3
ab
2 +
b3
6. (a
+ b
)4 a
4 +
4a
3b
+ 6
a2b
2 +
4ab
3 +
b4
No
w c
om
pa
re t
he c
oeff
icie
nts
of
the t
hree p
ro
du
cts
in
Ex
ercis
es 4
–6 w
ith
Pa
sca
l’s T
ria
ng
le.
7. D
esc
ribe t
he r
ela
tion
ship
betw
een
th
e e
xp
an
ded
form
of
(a +
b)n
an
d P
asc
al’s
Tri
an
gle
.
T
he c
oeff
icie
nts
of
the e
xp
an
ded
fo
rm a
re f
ou
nd
in
ro
w n
+ 1
of
Pascal’s
Tri
an
gle
.
8. U
se P
asc
al’s
Tri
an
gle
to w
rite
th
e e
xp
an
ded
form
of
(a +
b)6
.
a
6 +
6a
5b
+ 1
5a
4b
2 +
20a
3b
3 +
15
a2b
4 +
6ab
5 +
b6
1
1
1
1
2
1
1
3
3
1
1
4
6
4
1
7-7
Answers (Lesson 7-7)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A23 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
48
Gle
ncoe A
lgeb
ra 1
Sp
read
sheet
Act
ivit
y
Mu
ltip
lyin
g P
oly
no
mia
ls
Exerc
ises
Use t
he s
prea
dsh
eet
to f
ind
th
e v
alu
e o
f x t
ha
t a
llo
ws t
he b
ox
wit
h t
he g
rea
test
vo
lum
e f
or e
ach
pie
ce o
f ca
rd
bo
ard
. S
tate
th
e v
olu
me o
f th
e b
ox
.
1. 16 i
nch
es
lon
g a
nd
10 i
nch
es
wid
e
2. 24 i
nch
es
lon
g a
nd
18 i
nch
es
wid
e
2
; 144 i
n3
3;
648 i
n3
3. 28 i
nch
es
lon
g a
nd
16 i
nch
es
wid
e
4. 36 i
nch
es
lon
g a
nd
24 i
nch
es
wid
e
3
; 660 i
n3
5;
1820 i
n3
5. 48 i
nch
es
lon
g a
nd
48 i
nch
es
wid
e
6. 108 i
nch
es
lon
g a
nd
44 i
nch
es
wid
e
8
; 8192 i
n3
10;
21,1
20 i
n3
7. S
tud
y t
he s
pre
ad
sheet
you
cre
ate
d f
or
Exerc
ise 5
. S
up
pose
y i
s th
e v
olu
me o
f th
e b
ox
wit
h a
heig
ht
of
x i
nch
es.
If
you
were
to g
rap
h t
he o
rdere
d p
air
s (x
, y)
an
d c
on
nect
th
em
w
ith
a s
mooth
cu
rve,
wh
at
wou
ld y
ou
exp
ect
th
e g
rap
h t
o l
ook
lik
e?
Use
th
e g
rap
hin
g
tool
in t
he s
pre
ad
sheet
to v
eri
fy y
ou
r co
nje
ctu
re.
Sam
ple
an
sw
er:
Th
e g
rap
h
wo
uld
ris
e f
rom
(0,
0)
to t
he p
oin
t w
here
x g
ives t
he g
reate
st
vo
lum
e a
nd
th
en
fall b
ack d
ow
n t
ow
ard
th
e x
-axis
.
A
bo
x i
s m
ad
e b
y c
utt
ing
a s
qu
are w
ith
sid
es x
in
ch
es l
on
g f
ro
m e
ach
co
rn
er o
f a
pie
ce o
f ca
rd
bo
ard
an
d f
old
ing
up
th
e s
ides.
If t
he p
iece
of
ca
rd
bo
ard
is 1
5 i
nch
es l
on
g a
nd
12 i
nch
es w
ide,
wh
at
inte
ger v
alu
e o
f x a
llo
ws y
ou
to
ma
ke t
he b
ox
wit
h t
he
grea
test
vo
lum
e? W
ha
t is
th
e v
olu
me?
Ste
p 1
T
he f
inis
hed
box w
ill
be x
in
ches
hig
h,
12 -
2x i
nch
es
wid
e,
an
d 1
5 -
2x i
nch
es
lon
g.
Th
e v
olu
me o
f th
e b
ox
is x
(12 -
2x)(
15 -
2x)
cubic
in
ches.
Ste
p 2
U
se C
olu
mn
A o
f th
e s
pre
ad
sheet
for
the v
alu
e o
f x.
En
ter
the f
orm
ula
s fo
r th
e w
idth
, le
ngth
, an
d v
olu
me
in C
olu
mn
s C
, D
, an
d E
.
A
1 3 4 5 6 72
BC
DW
idth
Length
Volu
me
Heig
ht
10 8 6 4 2
13
11 9 7 5
130
176
162
112
50
1 2 3 4 5
Sh
eet
1S
heet
2S
heet
3
Noti
ce t
hat
x c
an
not
be g
reate
r th
an
5 b
eca
use
12 -
2x m
ust
be p
osi
tive.
In t
his
case
, th
e
box w
ith
th
e g
reate
st v
olu
me i
s 176 c
ubic
in
ches
wh
en
x =
2.
Exam
ple
xx
x
12-
2x
x
15-
2x
x
xx
xx
7-7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-8
Ch
ap
ter
7
49
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Sp
ecia
l P
rod
ucts
Sq
uare
s o
f Su
ms
an
d D
iffe
ren
ces
Som
e p
air
s of
bin
om
ials
have p
rod
uct
s th
at
foll
ow
sp
eci
fic
patt
ern
s. O
ne s
uch
patt
ern
is
call
ed
th
e s
qu
are
of
a s
um
. A
noth
er
is c
all
ed
th
e s
qu
are
of
a d
iffe
ren
ce.
Sq
uare
of
a s
um
(a +
b)2
= (
a +
b)(
a +
b) =
a2 +
2ab
+ b
2
Sq
uare
of
a d
iffe
ren
ce
(a -
b)2
= (
a -
b)(
a -
b) =
a2 -
2ab
+ b
2
F
ind
(3a
+ 4
)(3a
+ 4
).
Use
th
e s
qu
are
of
a s
um
patt
ern
, w
ith
a
= 3
a a
nd
b =
4.
(3
a +
4)(
3a
+ 4
) =
(3a
)2 +
2(3
a)(
4) +
(4
)2
=
9a
2 +
24a
+ 1
6
Th
e p
rod
uct
is
9a
2 +
24
a +
16.
F
ind
(2z -
9)(
2z -
9).
Use
th
e s
qu
are
of
a d
iffe
ren
ce p
att
ern
wit
h
a =
2z
an
d b
= 9
.
(2z -
9)(
2z -
9) =
(2z)2
- 2
(2z)
(9) +
(9)(
9)
=
4z2
- 3
6z +
81
Th
e p
rod
uct
is
4z2
- 3
6z +
81.
Exerc
ises
Fin
d e
ach
pro
du
ct.
1. (x
- 6
)2
2. (3
p +
4)2
3
. (4
x -
5)2
x
2 -
12
x +
36
9p
2 +
24p
+ 1
6
16
x2 -
40x +
25
4. (2
x -
1)2
5
. (2
h +
3)2
6
. (m
+ 5
)2
4
x2 -
4x +
1
4h
2 +
12h
+ 9
m
2 +
10
m +
25
7. (a
+ 3
)2
8. (3
- p
)2
9. (x
- 5
y)2
a
2 +
6a +
9
9 -
6p
+ p
2
x2 -
10
xy +
25
y2
10. (8
y +
4)2
11. (8
+ x
)2
12. (3
a -
2b)2
6
4y
2 +
64y +
16
64 +
16x +
x2
9a
2 -
12ab
+ 4
b2
13. (2
x -
8)2
14. (x
2 +
1)2
15. (m
2 -
2)2
4
x2 -
32x +
64
x4 +
2x
2 +
1
m4 -
4m
2 +
4
16. (x
3 -
1)2
17. (2
h2 -
k2)2
18. ( 1
−
4 x
+ 3) 2
x
6 -
2x
3+
1
4h
4 -
4h
2k
2 +
k4
1 −
16 x
2 +
3 −
2 x
+ 9
19. (x
- 4
y2)2
20. (2
p +
4r)
2
21. ( 2
−
3 x
- 2) 2
x
2 -
8xy
2 +
16y
4
4p
2 +
16p
r +
16
r2
4 −
9 x
2 -
8 −
3 x
+ 4
7-8
Exam
ple
1Exam
ple
2
Answers (Lesson 7-7 and Lesson 7-8)
Co
pyrig
ht ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f Th
e M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 7 A24 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
50
Gle
ncoe A
lgeb
ra 1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Sp
ecia
l P
rod
ucts
7-8 Exam
ple
Pro
du
ct o
f a
Su
m a
nd
a D
ifferen
ce
Th
ere
is
als
o a
patt
ern
for
the p
rod
uct
of
a
sum
an
d a
dif
fere
nce
of
the s
am
e t
wo t
erm
s, (
a +
b)(
a -
b).
Th
e p
rod
uct
is
call
ed
th
e
dif
feren
ce o
f sq
ua
res.
Pro
du
ct
of
a S
um
an
d a
Dif
fere
nce
(a +
b)(
a -
b) =
a2 -
b2
F
ind
(5x +
3y)(
5x -
3y).
(a
+ b
)(a
- b
) =
a2 -
b2
Pro
duct
of
a S
um
and a
Diffe
rence
(5x +
3y)(
5x -
3y) =
(5
x)2
- (
3y)2
a
= 5
x a
nd b
= 3
y
=
25x
2 -
9y
2
Sim
plif
y.
Th
e p
rod
uct
is
25
x2 -
9y
2.
Exerc
ises
Fin
d e
ach
pro
du
ct.
1. (x
- 4
)(x +
4)
2. ( p
+ 2
)( p
- 2
) 3. (4
x -
5)(
4x +
5)
x
2 -
16
p
2 -
4
16
x2 -
25
4. (2
x -
1)(
2x +
1)
5. (h
+ 7
)(h
- 7
) 6. (m
- 5
)(m
+ 5
)
4
x2 -
1
h2 -
49
m2 -
25
7. (2
d -
3)(
2d
+ 3
) 8. (3
- 5
q)(
3 +
5q
) 9. (x
- y
)(x +
y)
4
d2 -
9
9 -
25
q2
x2 -
y2
10. ( y
- 4
x)(
y +
4x)
11. (8
+ 4
x)(
8 -
4x)
12. (3
a -
2b
)(3a
+ 2
b)
y
2 -
16
x2
64 -
16x
2
9a
2 -
4b
2
13. (3
y -
8)(
3y +
8)
14. (x
2 -
1)(
x2 +
1)
15. (m
2 -
5)(
m2 +
5)
9
y2 -
64
x4 -
1
m4 -
25
16. (x
3 -
2)(
x3 +
2)
17. (h
2 -
k2)(
h2 +
k2)
18. ( 1
−
4 x
+ 2) ( 1
−
4 x
- 2)
x
6 -
4
h4 -
k4
1 −
16 x
2 -
4
19. (3
x -
2y
2)(
3x +
2y
2)
20. (2
p -
5r)
(2p
+ 5
r)
21. ( 4
−
3 x
- 2
y) ( 4
−
3 x
+ 2
y)
9
x2 -
4y
4
4p
2 -
25r2
16 −
9 x
2 -
4 y 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-8
Ch
ap
ter
7
51
Gle
ncoe A
lgeb
ra 1
Sk
ills
Pra
ctic
e
Sp
ecia
l P
rod
ucts
Fin
d e
ach
pro
du
ct.
1. (n
+ 3
)2
2. (x
+ 4
)(x +
4)
n
2 +
6n
+ 9
x
2 +
8x +
16
3. ( y -
7)2
4. (t
- 3
)(t -
3)
y
2 -
14y +
49
t2 -
6t +
9
5. (b
+ 1
)(b
- 1
) 6. (a
- 5
)(a
+ 5
)
b
2 -
1
a2 -
25
7. (p
- 4
)2
8. (z
+ 3
)(z -
3)
p
2 -
8p
+ 1
6
z2 -
9
9. (ℓ
+ 2
)(ℓ +
2)
10. (r
- 1
)(r -
1)
ℓ
2 +
4ℓ +
4
r2 -
2r +
1
11. (3
g +
2)(
3g -
2)
12. (2
m -
3)(
2m
+ 3
)
9
g2 -
4
4m
2 -
9
13. (6
+ u
)2
14. (r
+ t
)2
3
6 +
12u
+ u
2
r2 +
2rt
+ t
2
15. (3
q +
1)(
3q
- 1
) 16. (c
- d
)2
9
q2 -
1
c2 -
2cd
+ d
2
17. (2
k -
2)2
18. (w
+ 3
h)2
4
k2 -
8k +
4
w2 +
6w
h +
9h
2
19. (3
p -
4)(
3p
+ 4
) 20. (t
+ 2
u)2
9
p2 -
16
t2 +
4tu
+ 4
u2
21. (x
- 4
y)2
22. (3
b +
7)(
3b -
7)
x
2 -
8xy +
16
y2
9b
2 -
49
23. (3
y -
3g)(
3y +
3g)
24. (n
2 +
r2)2
9
y2 -
9g
2
n4 +
2n
2r2
+ r
4
25. (2
k +
m2)2
26. (3
t2 -
n)2
4
k2 +
4km
2 +
m4
9t4
- 6
t2n
+ n
2
27. G
EO
ME
TR
Y T
he l
en
gth
of
a r
ect
an
gle
is
the s
um
of
two w
hole
nu
mbers
. T
he w
idth
of
the r
ect
an
gle
is
the d
iffe
ren
ce o
f th
e s
am
e t
wo w
hole
nu
mbers
. U
sin
g t
hese
fact
s, w
rite
a
verb
al
exp
ress
ion
for
the a
rea o
f th
e r
ect
an
gle
. T
he a
rea i
s t
he s
qu
are
of
the
larg
er
nu
mb
er
min
us t
he s
qu
are
of
the s
maller
nu
mb
er.
7-8
Answers (Lesson 7-8)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he M
cG
raw
-Hill C
om
pan
ies,
Inc.
Chapter 7 A25 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
7
52
Gle
ncoe A
lgeb
ra 1
Practi
ce
Sp
ecia
l P
rod
ucts
Fin
d e
ach
pro
du
ct.
1. (n
+ 9
)2
2. (q
+ 8
)2
3. (x
- 1
0)2
n
2 +
18n
+ 8
1
q2 +
16
q +
64
x2 -
20x +
100
4. (r
- 1
1)2
5. ( p
+ 7
)2
6. (b
+ 6
)(b -
6)
r
2 -
22r +
121
p2 +
14
p +
49
b2 -
36
7. (z
+ 1
3)(z -
13)
8. (4j +
2)2
9. (5w
- 4
)2
z
2 -
169
1
6j2
+ 1
6j +
4
25w
2 -
40w
+ 1
6
10. (6h
- 1
)2
11. (3m
+ 4
)2
12. (7v -
2)2
3
6h
2 -
12h
+ 1
9
m2 +
24m
+ 1
6
49v
2 -
28
v +
4
13. (7k
+ 3
)(7k
- 3
) 14. (4d
- 7
)(4d
+ 7
) 15. (3g +
9h
)(3g -
9h
)
4
9k
2 -
9
16d
2 -
49
9
g2 -
81
h2
16. (4q
+ 5t)
(4q -
5t)
17. (a
+ 6u
)2
18. (5r +
s)2
1
6q
2 -
25t2
a
2 +
12au
+ 3
6u
2
25r2
+ 1
0rs
+ s
2
19. (6h
- m
)2
20. (k
- 6y)2
21. (u
- 7p
)2
3
6h
2 -
12h
m +
m2
k2 -
12ky +
36y
2
u2 -
14u
p +
49p
2
22. (4b
- 7v)2
23. (6n
+ 4p
)2
24. (5q
+ 6t)
2
1
6b
2 -
56b
v +
49v
2
36n
2 +
48
np
+ 1
6p
2
25q
2 +
60q
t +
36t2
25. (6a
- 7b)(
6a
+ 7b
) 26. (8h
+ 3d
)(8h
- 3d
) 27. (9x +
2y
2)2
3
6a
2 -
49b
2
64
h2 -
9d
2
81x
2 +
36
xy
2 +
4y
4
28. (3p
3 +
2m
)2
29. (5a
2 -
2b
)2
30. (4m
3 -
2t)
2
9
p6 +
12p
3m
+ 4
m2
25
a4 -
20a
2b
+ 4
b2
16
m6 -
16
m3t +
4t2
31. (6b
3 -
g)2
32. (2b
2 -
g)(
2b
2 +
g)
33. (2v
2 +
3x
2)(
2v
2 +
3x
2)
3
6b
6 -
12b
3g
+ g
2
4b
4 -
g2
4v
4 +
12v
2x
2 +
9x
4
34. G
EO
ME
TR
Y Jan
ell
e w
an
ts t
o e
nla
rge a
squ
are
gra
ph
th
at
she h
as
mad
e s
o t
hat
a s
ide
of
the n
ew
gra
ph
wil
l be 1
in
ch m
ore
th
an
tw
ice t
he o
rigin
al
sid
e g
. W
hat
trin
om
ial
rep
rese
nts
th
e a
rea o
f th
e e
nla
rged
gra
ph
? 4
g2 +
4g
+ 1
35. G
EN
ETIC
S In
a g
uin
ea p
ig,
pu
re b
lack
hair
colo
rin
g B
is
dom
inan
t over
pu
re w
hit
e
colo
rin
g b
. S
up
pose
tw
o h
ybri
d Bb g
uin
ea p
igs,
wit
h b
lack
hair
colo
rin
g,
are
bre
d.
a.
Fin
d a
n e
xp
ress
ion
for
the g
en
eti
c m
ak
e-u
p o
f th
e g
uin
ea p
ig o
ffsp
rin
g.
0.2
5B
B +
0.5
0B
b +
0.2
5b
b
b.
Wh
at
is t
he p
robabil
ity t
hat
two h
ybri
d g
uin
ea p
igs
wit
h b
lack
hair
colo
rin
g w
ill
pro
du
ce a
gu
inea p
ig w
ith
wh
ite h
air
colo
rin
g?
25%
7-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 7-8
Ch
ap
ter
7
53
Gle
ncoe A
lgeb
ra 1
1. P
RO
BA
BIL
ITY
T
he s
pin
ner
belo
w i
s d
ivid
ed
in
to 2
equ
al
sect
ion
s. I
f you
sp
in
the s
pin
ner
2 t
imes
in a
row
, th
e p
oss
ible
ou
tcom
es
are
sh
ow
n i
n t
he t
able
belo
w.
BLUE
RED
red
red
blu
e
red
red
blu
e
blu
e
blu
e
Wh
at
is t
he p
robabil
ity o
f sp
inn
ing a
blu
e a
nd
a r
ed
in
tw
o s
pin
s? 50%
2. G
RA
VIT
Y T
he h
eig
ht
of
a p
en
ny t
se
con
ds
aft
er
bein
g d
rop
ped
dow
n a
well
is
giv
en
by t
he p
rod
uct
of
(10 –
4t)
an
d
(10 +
4t)
. F
ind
th
e p
rod
uct
an
d s
imp
lify
. W
hat
typ
e o
f sp
eci
al
pro
du
ct d
oes
this
re
pre
sen
t?
100 -
16t2
; p
rod
uct
of
a s
um
an
d
dif
fere
nce
3. TR
AFFIC
PLA
NN
ING
T
he L
inco
ln
Mem
ori
al
in W
ash
ingto
n,
D.C
., i
s su
rrou
nd
ed
by a
cir
cula
r d
rive c
all
ed
L
inco
ln C
ircl
e.
Su
pp
ose
th
e N
ati
on
al
Park
Serv
ice w
an
ts t
o c
han
ge t
he l
ayou
t of
Lin
coln
Cir
cle s
o t
hat
there
are
tw
o
con
cen
tric
cir
cula
r ro
ad
s. W
rite
a
poly
nom
ial
equ
ati
on
for
the a
rea A
of
the
space
betw
een
th
e r
oad
s if
th
e r
ad
ius
of
the s
mall
er
road
is
10 m
ete
rs l
ess
th
an
th
e r
ad
ius
of
the l
arg
er
road
.
A =
20π
r -
10
0π
Lincoln
Mem
orial
4. B
US
INE
SS
T
he C
om
bo L
ock
Com
pan
y
fin
ds
that
its
pro
fit
data
fro
m 2
005 t
o t
he
pre
sen
t ca
n b
e m
od
ele
d b
y t
he f
un
ctio
n
y=
4n
2+
44n+
121,
wh
ere
y i
s th
e p
rofi
t n
years
sin
ce 2
005.
Wh
ich
sp
eci
al
pro
du
ct d
oes
this
poly
nom
ial
dem
on
stra
te?
Exp
lain
.
sq
uare
of
a s
um
; it
can
als
o b
e
wri
tten
as (
2n+
11)2
5. S
TO
RA
GE
A
cyli
nd
rica
l ta
nk
is
pla
ced
alo
ng a
wall
. A
cyli
nd
rica
l P
VC
pip
e w
ill
be h
idd
en
in
th
e c
orn
er
beh
ind
th
e t
an
k.
See t
he s
ide v
iew
dia
gra
m b
elo
w.
Th
e
rad
ius
of
the t
an
k i
s r
inch
es
an
d t
he
rad
ius
of
the P
VC
pip
e i
s s
inch
es.
Wall
Tank
Pipe
Floor
r-
s
r+
s
r-
s
a.
Use
th
e P
yth
agore
an
Th
eore
m t
o
wri
te a
n e
qu
ati
on
for
the r
ela
tion
ship
betw
een
th
e t
wo r
ad
ii.
Sim
pli
fy y
ou
r equ
ati
on
so t
hat
there
is
a z
ero
on
on
e
sid
e o
f th
e e
qu
als
sig
n.
0 =
r2 -
6rs
+ s
2
b.
Wri
te a
poly
nom
ial
equ
ati
on
you
cou
ld
solv
e t
o f
ind
th
e r
ad
ius s
of
the P
VC
p
ipe i
f th
e r
ad
ius
of
the t
an
k i
s 20
inch
es.
Wo
rd
Pro
ble
m P
racti
ce
Sp
ecia
l P
rod
ucts
7-8
0 =
s2 -
120
s +
400
Answers (Lesson 7-8)
ERROR: undefined
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