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5.3E: Exercises

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Practice Makes Perfect

Multiply Monomials

In the following exercises, multiply the monomials.

1. ⓐ (6y7)(3y4)(47rs2)(14rs3)

2. ⓐ (10x5)(3x3)(58x3y)(24x5y)

Answer

30x815x8y2

3. ⓐ (8u6)(9u)(23x2y)(34xy2)

4. ⓐ (6c4)(12c)(35m3n2)(59m2n3)

Answer

72c513m5n5

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

5. ⓐ8x(x2+2x15)5pq3(p22pq+6q2)

6. ⓐ 5t(t2+3t18)9r3s(r23rs+5s2)

Answer

5t315t2+90t
9sr527s2r4+45s3r3

7. ⓐ 8y(y2+2y15)4y2z2(3y2+12yzz2)

8. ⓐ 5m(m2+3m18)3x2y2(7x2+10xyy2)

Answer

5m315m2+90m
21x4y230x3y3+3x2y4

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using ⓐ the Distributive Property; ⓑ the FOIL method; ⓒ the Vertical Method.

9. (w+5)(w+7)

10. (y+9)(y+3)

Answer

y2+12y+27

11. (4p+11)(5p4)

12. (7q+4)(3q8)

Answer

21q244q32

In the following exercises, multiply the binomials. Use any method.

13. (x+8)(x+3)

14. (y6)(y2)

Answer

y28y+12

15. (2t9)(10t+1)

16. (6p+5)(p+1)

Answer

6p2+11p+5

17. (q5)(q+8)

18. (m+11)(m4)

Answer

m2+7m44

19. (7m+1)(m3)

20. (3r8)(11r+1)

Answer

33r285r8

21. (x2+3)(x+2)

22. (y24)(y+3)

Answer

y3+3y24y12

23. (5ab1)(2ab+3)

24. (2xy+3)(3xy+2)

Answer

6x2y2+13xy+6

25. (x2+8)(x25)

26. (y27)(y24)

Answer

y411y2+28

27. (6pq3)(4pq5)

28. (3rs7)(3rs4)

Answer

9r2s233rs+28

Multiply a Polynomial by a Polynomial

In the following exercises, multiply using ⓐ the Distributive Property; ⓑ the Vertical Method.

29. (x+5)(x2+4x+3)

30. (u+4)(u2+3u+2)

Answer

u3+7u2+14u+8

31. (y+8)(4y2+y7)

32. (a+10)(3a2+a5)

Answer

3a3+31a2+5a50

33. (y23y+8)(4y2+y7)

34. (2a25a+10)(3a2+a5)

Answer

6a413a3+15a2+35a50

Multiply Special Products

In the following exercises, multiply. Use either method.

35. (w7)(w29w+10)

36. (p4)(p26p+9)

Answer

p310p2+33p36

37. (3q+1)(q24q5)

38. (6r+1)(r27r9)

Answer

6r341r261r9

In the following exercises, square each binomial using the Binomial Squares Pattern.

39. (w+4)2

40. (q+12)2

Answer

q2+24q+144

41. (3xy)2

42. (2y3z)2

Answer

4y212yz+9z2

43. (y+14)2

44. (x+23)2

Answer

x2+43x+49

45. (15x17y)2

46. (18x19y)2

Answer

164x2136xy+181y2

47. (3x2+2)2

48. (5u2+9)2

Answer

25u4+90u2+81

49. (4y32)2

50. (8p33)2

Answer

64p648p3+9

In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.

51. (5k+6)(5k6)

52. (8j+4)(8j4)

Answer

64j216

53. (11k+4)(11k4)

54. (9c+5)(9c5)

Answer

81c225

55. (9c2d)(9c+2d)

56. (7w+10x)(7w10x)

Answer

49w2100x2

57. (m+23n)(m23n)

58. (p+45q)(p45q)

Answer

p21625q2

59. (ab4)(ab+4)

60. (xy9)(xy+9)

Answer

x2y281

61. (12p311q2)(12p3+11q2)

62. (15m28n4)(15m2+8n4)

Answer

225m464n8

In the following exercises, find each product.

63. (p3)(p+3)

64. (t9)2

Answer

t218t+81

65. (m+n)2

66. (2x+y)(x2y)

Answer

2x23xy2y2

67. (2r+12)2

68. (3p+8)(3p8)

Answer

9p264

69. (7a+b)(a7b)

70. (k6)2

Answer

k212k+36

71. (a57b)2

72. (x2+8y)(8xy2)

Answer

8x3x2y2+64xy8y3

73. (r6+s6)(r6s6)

74. (y4+2z)2

Answer

y8+4y4z+4z2

75. (x5+y5)(x5y5)

76. (m38n)2

Answer

m616m3n+64n2

77. (9p+8q)2

78. (r2s3)(r3+s2)

Answer

r5+r2s2r3s3s5

Mixed Practice

79. (10y6)+(4y7)

80. (15p4)+(3p5)

Answer

18p9

81. (x24x34)(x2+7x6)

82. (j28j27)(j2+2j12)

Answer

10j15

83. (15f8)(20f3)

84. (14d5)(36d2)

Answer

9d7

85. (4a3b)(9a2b6)

86. (6m4n3)(7mn5)

Answer

72m5n8

87. 5m(m2+3m18)

88. 5q3(q22q+6)

Answer

5q510q4+30q3

89. (s7)(s+9)

90. (y22y)(y+1)

Answer

y3y22y

91. (5xy)(x4)

92. (6k1)(k2+2k4)

Answer

6k311k226k+4

93. (3x11y)(3x11y)

94. (11b)(11+b)

Answer

121b2

95. (rs27)(rs+27)

96. (2x23y4)(2x2+3y4)

Answer

4x49y8

97. (m15)2

98. (3d+1)2

Answer

9d2+6d+1

99. (4a+10)2

100. (3z+15)2

Answer

9z265z+125

Multiply Polynomial Functions

101. For functions f(x)=x+2 and g(x)=3x22x+4, find ⓐ (f·g)(x)(f·g)(1)

102. For functions f(x)=x1 and g(x)=4x2+3x5, find ⓐ (f·g)(x)(f·g)(2)

Answer

(f·g)(x)=4x3x28x+5
(f·g)(2)=15

103. For functions f(x)=2x7 and g(x)=2x+7, find ⓐ (f·g)(x)(f·g)(3)

104. For functions f(x)=7x8 and g(x)=7x+8, find ⓐ (f·g)(x)(f·g)(2)

Answer

(f·g)(x)=49x264
(f·g)(2)=187

105. For functions f(x)=x25x+2 and g(x)=x23x1, find ⓐ (f·g)(x)(f·g)(1)

106. For functions f(x)=x2+4x3 and g(x)=x2+2x+4, find ⓐ (f·g)(x)(f·g)(1)

Answer

(f·g)(x)=x4+6x3+9x2+10x12(f·g)(1)=14

Writing Exercises

107. Which method do you prefer to use when multiplying two binomials: the Distributive Property or the FOIL method? Why? Which method do you prefer to use when multiplying a polynomial by a polynomial: the Distributive Property or the Vertical Method? Why?

108. Multiply the following:

(x+2)(x2)

(y+7)(y7)

(w+5)(w5)

Explain the pattern that you see in your answers.

Answer

Answers will vary.

109. Multiply the following:

(p+3)(p+3)

(q+6)(q+6)

(r+1)(r+1)

Explain the pattern that you see in your answers.

110. Why does (a+b)2 result in a trinomial, but (ab)(a+b) result in a binomial?

Answer

Answers will vary.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?


This page titled 5.3E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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