Name ——————————————————————— Date ————————————

Copy

right

© H

ough

ton

Miffl

in H

arco

urt P

ublis

hing

Com

pany

. All

right

s re

serv

ed.

Practice CFor use with the lesson “Multiply Polynomials”

Find the product.

1. 28y3(2y4 2 5y2 1 3) 2. (b 1 3)(3b2 2 2b 1 1) 3. (6w 2 3)(4 2 3w)

4. (9m3 1 1)(4m2 2 1) 5. (2x2 1 5x 2 2)(x 1 3) 6. (8n2 2 1)(3n2 2 4n 1 5)

7. (3p4 2 5)(2p2 1 4) 8. (28r3 1 2)(6r2 2 1) 9. (25z2 2 3)(22z2 1 9)

10. xy(x2 1 2y) 11. 23x(2xy 1 5y) 12. y2(x2y 1 y2x)

13. (x 2 y)(5x 1 6y) 14. (xy2 1 70)(3x 1 2y) 15. (x2 2 4xy 1 y2)(5xy)

Simplify the expression.

16. (7n 1 1)(3n 1 5) 1 (4n 2 2)(3n 1 1) 17. 5w2(3w3 2 2w 1 1) 1 w4(w2 2 2w 1 3)

Write a polynomial for the area of the shaded region.

18.

x 1 4

x 1 3

19.

8

12

x 1 1

2x

20. Car Production During the period 1995–2002, the number of cars C (in thousands) produced in the U.S. and the average price P (in dollars) spent on one of these cars can be modeled by

C 5 2198.02t 1 6320.49 and P 5 1.67t4 2 22.28t3 1 44.84t2 1 531.16t 1 16,860

where t is the number of years since 1995.

a. Write an equation that models the total amount spent (in thousands of dollars) on new cars in the U.S. by consumers as a function of the number of years since 1995.

b. How much money was spent in the U.S. on new cars by consumers in 1995?

21. Sporting Goods Equipment During the period 1990–2002, the amount of money E (in millions of dollars) spent on sporting goods equipment in the U.S. and the percent P (in decimal form) of this amount that is spent on exercise equipment can be modeled by

E 5 25.56t4 1 149.93t3 2 1314.65t2 1 4396.75t 1 14,439.09

and P 5 20.00002t4 2 0.0005t3 1 0.0028t2 1 0.001t 1 0.126

where t is the number of years since 1990.

a. Find the values of E and P for t 5 0. What does the product E p P mean for t = 0 in the context of this problem?

b. Write an equation that models the amount spent (in millions of dollars) on exercise equipment as a function of the number of years since 1990.

c. How much money was spent in the U.S. on exercise equipment in 1990?

Algebra 1Chapter Resource Book8-20

Les

so

n 8

.2

Lesson

8.2

CS10_CC_A1_MECR710730_C8L02PC.indd 20 5/14/11 12:18:50 AM

Copy

right

© H

ough

ton

Miffl

in H

arco

urt P

ublis

hing

Com

pany

. All

right

s re

serv

ed.

an

sw

er

s

Lesson Add and Subtract Polynomials, continued

Challenge Practice

1. x 1 x 1 4 5 2x 14 5 2(x 1 2); Because the number of quarters and dimes is a multiple of 2, it is even. 2. x 1 2x 1 1 5 3x 11; If x is even, then 3x is even and 3x 1 1 is odd. If x is odd, then 3x is odd and 3x 1 1 is even. So, whether the total number of coins is even or odd can’t be determined. 3. x 1 3x 1 5 5 4x 1 5; Whether x is even or odd, 4x is even, so 4x 1 5 is odd.

4. x 1 4 1 3x 1 5 5 4x 1 9; Whether x is even or odd, 4x is even, so 4x 1 9 is odd.

5. x 1 4 1 2x 1 1 1 3x 1 5 5 6x 1 10 5 2(x 1 5); Because the number of dimes, nickels, and pennies is a multiple of 2, it is even.

6. 0 7. 1 8. x 9. 3 10. 81

} 4 11. 25 12. 19

Lesson Multiply Polynomials

Teaching Guide

1. Distributive property

2. (5 1 3)(7 1 2) 5 5(7) 1 5(2) 1 3(7) 1 3(2)

5 72

3. The degree of the product of two polynomials of degrees m and n is m 1 n because of the product of powers property of exponents.

4. No; Sample answer: 3x3 1 2x 1 2

Practice Level A

1. 3x3 2 2x2 1 x 2. 6y4 1 2y3 2 8y

3. 23m3 2 12m2 1 3m 4. 4d4 2 3d3 1 d2

5. 2w5 2 3w4 6. 2a4 2 3a3 1 a2

7. x2 2 3x 2 4 8. y2 1 8y 1 12

9. a2 2 8a 1 15 10. 2m2 1 7m 1 3

11. 3z2 2 11z 2 20 12. 3d2 1 17d 2 6

13. y2 1 5y 2 24 14. n2 1 11n 1 30

15. 3x2 1 13x 2 10 16. 8a2 2 2a 2 1

17. w3 1 3w2 1 3w 1 1

18. m3 2 4m2 1 7m 2 6 19. 8y2 2 23y 2 3

20. 15b2 1 7b 2 2 21. 6d2 2 14d 1 4

22. 6x2 1 8x 1 2 23. 6x2 1 22x 2 8

24. 2s2 1 s 2 15 25. 40c2 2 46c 2 14

26. 16p2 2 46p 1 15 27. 14t2 1 26t 2 4

28. a. V 5 288x2 1 1152x 1 1152 b. 41,472 in.3

29. a. A: 76,226; P: 0.6; A p P indicates the num-ber of acres (in thousands) that are parks. b. A p P 5 20.1688t3 2 59.0818t2 1 812.634t 1 45,735.6

Practice Level B

1. 6x4 2 3x3 2 x2 2. 220a7 1 15a4 2 5a3

3. 28d5 1 20d4 2 24d3 1 8d2

4. 6x2 2 13x 2 5 5. 2y2 2 7y 2 15

6. 24a2 2 18a 1 3 7. 5b2 2 42b 1 16

8. 16m2 1 38m 1 21 9. 23p3 1 6p2 2 p 1 2

10. 22z2 1 13z 2 21 11. 26d2 1 23d 2 10

12. n3 1 5n2 1 9n 1 5 13. w3 1 5w2 2 23w 2 3

14. 2s3 1 11s2 1 13s 2 5

15. 5x3y 2 20x2y2 1 5xy3 16. 4a2 1 a 2 1

17. 23x2 2 8x 1 10 18. 2m2 1 5m 2 41

19. 3x2 1 15x 20. x2 1 6x 1 8

21. a. A 5 4x2 1 22x 1 30 b. 72 ft2

22. a. S: 66,939; P: 0.4; S p P indicates the number of students (in thousands) who were between 7 and 13 in 1995. b. S p P 5 0.000163t7 2 0.01166225t6 1 0.218856t5 2 1.510115t4 1 0.46605t3 1 38.8676t2 1 181.107t 1 26,775.6 c. about 26,775,600

Practice Level C

1. 216y7 1 40y5 2 24y3 2. 3b3 1 7b2 2 5b 1 3

3. 218w2 1 33w 2 12

4. 36m5 2 9m3 1 4m2 2 1

5. 2x3 1 11x2 1 13x 2 6

6. 24n4 2 32n3 1 37n2 1 4n 2 5

7. 6p6 2 12p4 2 10p2 1 20

8. 248r5 1 8r3 1 12r2 2 2 9. 10z4 2 39z2 2 27

10. x3y 1 2xy2 11. 26x2y 2 15xy

12. x2y3 1 xy4 13. 5x2 1 xy 2 6y2

14. 2xy3 1 3x2y2 1 210x 1 140y

15. 5x3y 2 20x2y2 1 5xy3 16. 33n2 1 36n 1 3

17. w6 1 13w5 1 3w4 2 10w3 1 5w2

18. 1 }

2 x2 1

7 } 2 x 1 6 19. 22x2 2 2x 1 96

20. a. A 5 2330.6934t5 1 14,967.1039t4 2 149,699.734t3 1 178,230.4684t2 1 18,574.268t 1 106,563,461.4 b. $106,563,461,400

21. a. E: 14,439.09; P: 0.126; E p P indicates the amount of money (in millions of dollars) spent on exercise equipment.

Algebra 1Chapter Resource Book A13

8.1

8.2

CS10_CC_A1_MECR710730_C8AK.indd 13 5/21/11 2:40:42 AM

Copy

right

© H

ough

ton

Miffl

in H

arco

urt P

ublis

hing

Com

pany

. All

right

s re

serv

ed.

an

sw

er

s

Lesson Multiply Polynomials, continuedb. E p P 5 0.0001112t8 2 0.0002186t7 2 0.06424t6 1 0.983634t5 2 6.7188068t4 1 22.667885t3 2 120.819698t2 1 568.42959t 1 1819.32534 c. $1,819,325,340

Study Guide

1. 21x4 2 6x3 1 9x2

2. 12x8 2 8x7 2 32x6 1 36x5

3. 3m3 1 17m2 1 6m 2 4 4. 6n2 1 29n 1 28

5. 2p3 1 13p2 2 p 1 42

6. 12q3 2 28q2 1 7q 1 12 7. 15t2 2 13t 2 72

8. 72s2 2 119s 1 49 9. 2y21 15y 2 27

Real-Life Application

1. 60x2 1 48x 1 9 2. x2 2 4

3. 59x2 1 48x 1 13

4. x (feet) 6 9 12

Total area of lawn (sq ft)

2457 5301 9225

Area of dog cage (sq ft)

32 77 140

Area of lawn mowed (sq ft)

2425 5224 9085

5. No. The total area of the lawn when x 5 6 is 2457 feet. When x 5 12 the total area of the lawn is 9225 square feet, which is not double 2457 square feet.

Challenge Practice

1. x7 1 3x5 1 2x3 2. 2y7 1 3y5 2 y4 1 3y2

3. 2x7 1 4x3y3 1 2x4y 1 4y4

4. 2x12 1 11x10 1 12x8

5. x5 1 2x4 1 3x3 1 6x2 1 2x 1 4 6. 0

7. 4x 8. 4x2 9. 2x3 2 x2 2 6x 1 1

10. 2x3 1 8x2 1 5

11. V 5 9x(50x 1 150) (8x 1 16)

12. V 5 3600x3 1 18,000x2 1 21,600x

13. 168 trailers

Lesson Find Special Products of Polynomials

Teaching Guide

1. x2 2 4, x2 2 36, 4x2 2 1The factors in the expression are a sum and difference of two terms. The product is the difference of the squares of the two terms.

2. x2 1 6x 1 9, x2 1 14x 1 49, 4x2 1 12x 1 9The expression is the square of a sum of two terms. The product is the square of the first plus twice the product of the two terms plus the square of the second.

3. x2 2 2x 1 1, x2 2 4x 1 4, 9x2 2 24x 1 16 The expression is the square of a difference of two terms. The product is the square of the first minus twice the product of the two terms plus the square of the second.

Practice Level A

1. 2ab 2. 2mn 3. 2x 4. 10x 5. y2 6. 9

7. C 8. A 9. B 10. x2 1 8x 1 16

11. m2 2 16m 1 64 12. a2 1 20a 1 100

13. p2 2 24p 1 144 14. 4y2 1 4y 1 1

15. 9y2 2 6y 1 1 16. 100r2 2 20r 1 1

17. 16n2 1 16n 1 4 18. 9c2 2 12c 1 4

19. z2 2 25 20. b2 2 4 21. n2 2 64

22. a2 2 100 23. 4x2 2 1 24. 25m2 2 1

25. 16d2 2 1 26. 9p2 2 4 27. 4r2 2 9

28. Find the product (10 2 3)(10 1 3).

29. Find the product (30 2 6)(30 1 6).

30. Find the product (60 1 9)(60 2 9).

31. T 5 9t2 2 4 32. a. 0.25B2 1 0.5Bb 1 0.25b2 b. 25%

Practice Level B

1. x2 2 18x 1 81 2. m2 1 22m 1 121

3. 25s2 1 20s 1 4 4. 9m2 1 42m 1 49

5. 16p2 2 40p 1 25 6. 49a2 2 84a 1 36

7. 100z2 2 60z 1 9 8. 4x2 1 4xy 1 y2

9. 9y2 2 6xy 1 x2 10. a2 2 81

11. z2 2 400 12. 25r2 2 1 13. 36m2 2 100

14. 49p2 2 4 15. 81c2 2 1 16. 16x2 2 9

17. 2w2 1 16 18. 24y2 1 25 19. Find the product (20 2 5)(20 1 5). 20. Find the product (50 2 7)(50 1 7). 21. Find the product (20 2 2)2.

22. 16x2 2 0.25 23. 16x2 1 4x 1 0.25

Algebra 1Chapter Resource BookA14

8.2 8.3

CS10_CC_A1_MECR710730_C8AK.indd 14 5/21/11 2:40:43 AM