5.3E: Exercises
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- Mar 28, 2021
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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
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ⓐ30x8 ⓑ 15x8y2
3. ⓐ (−8u6)(−9u) ⓑ (23x2y)(34xy2)
4. ⓐ (−6c4)(−12c) ⓑ (35m3n2)(59m2n3)
- Answer
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ⓐ 72c5 ⓑ 13m5n5
Multiply a Polynomial by a Monomial
In the following exercises, multiply.
5. ⓐ−8x(x2+2x−15) ⓑ 5pq3(p2−2pq+6q2)
6. ⓐ −5t(t2+3t−18) ⓑ 9r3s(r2−3rs+5s2)
- Answer
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ⓐ −5t3−15t2+90t
ⓑ 9sr5−27s2r4+45s3r3
7. ⓐ −8y(y2+2y−15) ⓑ −4y2z2(3y2+12yz−z2)
8. ⓐ −5m(m2+3m−18) ⓑ −3x2y2(7x2+10xy−y2)
- Answer
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ⓐ −5m3−15m2+90m
ⓑ −21x4y2−30x3y3+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
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y2+12y+27
11. (4p+11)(5p−4)
12. (7q+4)(3q−8)
- Answer
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21q2−44q−32
In the following exercises, multiply the binomials. Use any method.
13. (x+8)(x+3)
14. (y−6)(y−2)
- Answer
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y2−8y+12
15. (2t−9)(10t+1)
16. (6p+5)(p+1)
- Answer
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6p2+11p+5
17. (q−5)(q+8)
18. (m+11)(m−4)
- Answer
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m2+7m−44
19. (7m+1)(m−3)
20. (3r−8)(11r+1)
- Answer
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33r2−85r−8
21. (x2+3)(x+2)
22. (y2−4)(y+3)
- Answer
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y3+3y2−4y−12
23. (5ab−1)(2ab+3)
24. (2xy+3)(3xy+2)
- Answer
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6x2y2+13xy+6
25. (x2+8)(x2−5)
26. (y2−7)(y2−4)
- Answer
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y4−11y2+28
27. (6pq−3)(4pq−5)
28. (3rs−7)(3rs−4)
- Answer
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9r2s2−33rs+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
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u3+7u2+14u+8
31. (y+8)(4y2+y−7)
32. (a+10)(3a2+a−5)
- Answer
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3a3+31a2+5a−50
33. (y2−3y+8)(4y2+y−7)
34. (2a2−5a+10)(3a2+a−5)
- Answer
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6a4−13a3+15a2+35a−50
Multiply Special Products
In the following exercises, multiply. Use either method.
35. (w−7)(w2−9w+10)
36. (p−4)(p2−6p+9)
- Answer
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p3−10p2+33p−36
37. (3q+1)(q2−4q−5)
38. (6r+1)(r2−7r−9)
- Answer
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6r3−41r2−61r−9
In the following exercises, square each binomial using the Binomial Squares Pattern.
39. (w+4)2
40. (q+12)2
- Answer
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q2+24q+144
41. (3x−y)2
42. (2y−3z)2
- Answer
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4y2−12yz+9z2
43. (y+14)2
44. (x+23)2
- Answer
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x2+43x+49
45. (15x−17y)2
46. (18x−19y)2
- Answer
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164x2−136xy+181y2
47. (3x2+2)2
48. (5u2+9)2
- Answer
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25u4+90u2+81
49. (4y3−2)2
50. (8p3−3)2
- Answer
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64p6−48p3+9
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.
51. (5k+6)(5k−6)
52. (8j+4)(8j−4)
- Answer
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64j2−16
53. (11k+4)(11k−4)
54. (9c+5)(9c−5)
- Answer
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81c2−25
55. (9c−2d)(9c+2d)
56. (7w+10x)(7w−10x)
- Answer
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49w2−100x2
57. (m+23n)(m−23n)
58. (p+45q)(p−45q)
- Answer
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p2−1625q2
59. (ab−4)(ab+4)
60. (xy−9)(xy+9)
- Answer
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x2y2−81
61. (12p3−11q2)(12p3+11q2)
62. (15m2−8n4)(15m2+8n4)
- Answer
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225m4−64n8
In the following exercises, find each product.
63. (p−3)(p+3)
64. (t−9)2
- Answer
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t2−18t+81
65. (m+n)2
66. (2x+y)(x−2y)
- Answer
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2x2−3xy−2y2
67. (2r+12)2
68. (3p+8)(3p−8)
- Answer
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9p2−64
69. (7a+b)(a−7b)
70. (k−6)2
- Answer
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k2−12k+36
71. (a5−7b)2
72. (x2+8y)(8x−y2)
- Answer
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8x3−x2y2+64xy−8y3
73. (r6+s6)(r6−s6)
74. (y4+2z)2
- Answer
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y8+4y4z+4z2
75. (x5+y5)(x5−y5)
76. (m3−8n)2
- Answer
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m6−16m3n+64n2
77. (9p+8q)2
78. (r2−s3)(r3+s2)
- Answer
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r5+r2s2−r3s3−s5
Mixed Practice
79. (10y−6)+(4y−7)
80. (15p−4)+(3p−5)
- Answer
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18p−9
81. (x2−4x−34)−(x2+7x−6)
82. (j2−8j−27)−(j2+2j−12)
- Answer
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−10j−15
83. (15f8)(20f3)
84. (14d5)(36d2)
- Answer
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9d7
85. (4a3b)(9a2b6)
86. (6m4n3)(7mn5)
- Answer
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72m5n8
87. −5m(m2+3m−18)
88. 5q3(q2−2q+6)
- Answer
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5q5−10q4+30q3
89. (s−7)(s+9)
90. (y2−2y)(y+1)
- Answer
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y3−y2−2y
91. (5x−y)(x−4)
92. (6k−1)(k2+2k−4)
- Answer
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6k3−11k2−26k+4
93. (3x−11y)(3x−11y)
94. (11−b)(11+b)
- Answer
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121−b2
95. (rs−27)(rs+27)
96. (2x2−3y4)(2x2+3y4)
- Answer
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4x4−9y8
97. (m−15)2
98. (3d+1)2
- Answer
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9d2+6d+1
99. (4a+10)2
100. (3z+15)2
- Answer
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9z2−65z+125
Multiply Polynomial Functions
101. For functions f(x)=x+2 and g(x)=3x2−2x+4, find ⓐ (f·g)(x) ⓑ (f·g)(−1)
102. For functions f(x)=x−1 and g(x)=4x2+3x−5, find ⓐ (f·g)(x) ⓑ (f·g)(−2)
- Answer
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ⓐ (f·g)(x)=4x3−x2−8x+5
ⓑ (f·g)(−2)=−15
103. For functions f(x)=2x−7 and g(x)=2x+7, find ⓐ (f·g)(x) ⓑ (f·g)(−3)
104. For functions f(x)=7x−8 and g(x)=7x+8, find ⓐ (f·g)(x) ⓑ (f·g)(−2)
- Answer
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ⓐ (f·g)(x)=49x2−64
ⓑ (f·g)(−2)=187
105. For functions f(x)=x2−5x+2 and g(x)=x2−3x−1, find ⓐ (f·g)(x) ⓑ (f·g)(−1)
106. For functions f(x)=x2+4x−3 and g(x)=x2+2x+4, find ⓐ (f·g)(x) ⓑ (f·g)(1)
- Answer
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ⓐ (f·g)(x)=x4+6x3+9x2+10x−12 ⓑ (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)(x−2)
(y+7)(y−7)
(w+5)(w−5)
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 (a−b)(a+b) result in a binomial?
- Answer
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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?