algebra 1b unit 08 08 alg 1b notes chap 8.pdfnotes – part b section 8-2: dividing monomials...
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Algebra 1B
Unit 08 Sections 8.1-8.2,8.4-8.7
GUIDED NOTES
NAME _________________________
Teacher _______________
Period ___________
1
Date: ______________________
Notes – Part A Section 8-1: Multiplying Monomials
Monomial:
MULTIPLY MONOMIALS
Constant: Example #1:
Determine if each expression is a monomial. Explain your reasoning.
1.) 17 – s 2.) 8f2
g
3.) ¾ 4.) xy
5.) hk
6.) p + q
7.) x 8.) abc8
5
2
Product of Powers: Example #2:
Simplify each expression. Show all work!
1.) (r4) (- 12r7) 2.) (6cd) (5c5d2
)
3.) (5x7) (x6) 4.) (4ab6) (- 7 a2b3
)
3
Date: ______________________
Notes – Part B Section 8-1: Multiplying Monomials
POWERS OF MONOMIALS
Power of a Power: Example #1:
Simplify each expression. Show all work!
1.) { [ (-3)2 ]3 } 2 2.) [ (23)3 ]
2
3.) [ (23)2 ] 3 4.) [ (33)2 ]
4
4
Power of a Product: Example #2:
Simplify each expression. Show all work!
1.) (3y5z)2 2.) (5xyz)
3
3.) (x2y5)3 4.) 2 (a4b2)7
5
Date: ______________________
Notes – Part A Section 8-2: Dividing Monomials
QUOTIENTS OF MONOMIALS
Quotient of Powers: Example #1:
Simplify each expression. Show all work!
1.) a bab
5 8
3 2.) x yx y
7 12
6 3
3.) 77
8
3 4.) −510
7
6 3
pqp q
6
Negative Exponents: Example #2:
Simplify each expression. Show all work!
1.) b cd
−
−
3 2
5 2.) − −
−
321
4 7
2 7 5
a ba b c
3.) x
y z
−
−
6
4 9 4.) 75
15
3 5
5 4 8
j kj k l
−
− −
7
Date: ______________________
Notes – Part B Section 8-2: Dividing Monomials
QUOTIENTS OF EXPONENTS
Zero Exponent: Example #1:
Simplify each expression. Show all work!
1.) −
38
5
7
0x yxy
2.) t st
3 0
2
3.) 128
8 7
5 10
0m n
m n
4.)
b cc
0 8
2
8
Power of a Quotient: Example #2:
Simplify each expression. Show all work!
1.) 2
3
2 4p
2.)
45
3 2
4 7
3c de f
3.) 27
3
2
3c dz
4.)
25
5
7
3x yxy
−
9
Date: ______________________
Notes Section 8-4: Polynomials
DEGREE OF POLYNOMIAL
Polynomial: Example #1:
State whether each expression is a polynomial. If yes, identify it as a monomial, binomial, or trinomial.
1.) 6 – 4 2.) x2
+ 2xy – 7
3.) 26b514 19
5
2
4
d ed+
4.)
5.) 2x – 3yz 6.) 8n3 + 5n
-2
7.) - 8 8.) 4n2
+ 5a + a + 9
10
Degree of a Polynomial: Example #2:
9.) 12 + 5b + 6bc + 8bc
Find the degree of each polynomial.
2
10.) 9x2
– 2x – 4
11.) 14g2h5
i
12.) 5mn
2
13.) -4x2y2 + 3x2
+ 5
14.) 3a + 7ab – 2a2
b + 16
Example #3:
Arrange the terms of each polynomial so that the powers of x are in ascending order.
15.) 16 + 14x3 + 2x – x
2
16.) 7y2 + 4x3 + 2xy3 – x2y
2
17.) 7x2 + 2x4
– 11
18.) 2xy3 + 5x3 – y2 – 3x2
y
Example #4:
Arrange the terms of each polynomial so that the powers of x are in descending order.
19.) 6x2 + 5 – 8x – 2x
3
20.) 3a3x2 – a4 + 4ax5 + 9a2
x
21.) 8 + 7x2 – 12xy3 – 4x3
y
22.) a4 + ax2 – 2a3xy3 – 9x4
y
11
Date: ______________________
Notes Section 8-5: Adding and Subtracting Polynomials
ADD POLYNOMIALS
Example 1: Find (3x2 – 4x + 8) + (2x – 7x2
– 5). Show all work!
Example 2: Find (7y2 + 2y – 3) + (2 – 4y + 5y2
). Show all work!
Example 3:3 2 1
4 3
2
2
x xx x
− +
+ + − Find . Show all work!
Example 4:2 56 2 3
2
2
xx x+
+ − + Find . Show all work!
12
SUBTRACT POLYNOMIALS
Example 5: Find (3n2 + 13n3 + 5n) - (7n +4n3
). Show all work!
Example 6: Find (6y2 + 8y4 – 5y) - (9y4 – 7y + 2y2
). Show all work!
Example 7:5 42 3xx+
− − +( ) Find . Show all work!
Example 8:8 4
6 32
xx x+
− − +( ) Find . Show all work!
13
Date: ______________________
Notes – Part A Section 8-6: Multiplying a Polynomial by a Monomial
PRODUCT OF MONOMIAL AND POLYNOMIAL
Example 1: Find – 2x2 (3x2
– 7x + 10). Show all work!
Example 2: Find 6y (4y2
– 9y – 7). Show all work!
Example 3: Find -4xy (5x2 – 12xy + 7y2
). Show all work!
14
Example 4: Simplify 4 (3d2 + 5d) – d (d2
– 7d + 12). Show all work!
Example 5: Simplify 3 (2t2
– 4t – 15) + 6t (5t + 2). Show all work!
Example 6: Simplify 5n (4n3 + 6n2 – 2n + 3) – 4 (n2 + 7n). Show all work!
15
Date: ______________________
Notes – Part B Section 8-6: Multiplying a Polynomial by a Monomial
SOLVE EQUATONS WITH POLYNOMIAL EXPRESSIONS
Example 1:
Solve y (y – 12) + y (y + 2) + 25 = 2y (y + 5) – 15. Show all work!
Example 2:
Solve b (12 + b) – 7 = 2b + b (-4 + b). Show all work!
16
Example 3:
Solve -2 (w + 1) + w = 7 – 4w. Show all work!
Example 4: Solve x (x + 2) – 3x = x (x – 4) + 5. Show all work!
17
Date: ______________________
Notes – Part A Section 8-7: Multiplying Polynomials
MULTIPLY BINOMIALS
Example 1:( )( )xx+
× +32
Find . Show all work!
Example 2:( )( )yy+
× −84
Find . Show all work!
18
Example 3:( )
( )xx−
× +7
6 4 Find . Show all work!
Example 4:( )
( )9 1
3 2p
p−
× − Find . Show all work!
19
Date: ______________________
Notes – Part B Section 8-7: Multiplying Polynomials
F – O – I – L:
MULTIPLY BINOMIALS
Example 1:
Find (z – 6) ( z – 12). Show all work!
Example 2:
Find (x – 5) (x + 7). Show all work!
Example 3:
Find (2y + 3) (6y -7). Show all work!
Example 4:
Find (5x – 4) (2x + 8). Show all work!
20
MULTIPLY POLYNOMIALS
Example #5:
Find each product. Show all work! (Hint: Use the Distributive Property)
a.) (4x + 9) (2x2
– 5x + 3)
b.) (y2 – 2y + 5) (6y2 – 3y + 1)
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