Exercises: Multiply Polynomials (5.3)

Exercises: Multiply a Polynomial by a Monomial

Instructions: For questions 1-64, multiply.
1. [latex]4\left(w+10\right)[/latex]
Solution

[latex]4w+40[/latex]

2. [latex]6\left(b+8\right)[/latex]
3. [latex]-3\left(a+7\right)[/latex]
Solution

[latex]-3a-21[/latex]


4. [latex]-5\left(p+9\right)[/latex]
5. [latex]2\left(x-7\right)[/latex]
Solution

[latex]2x-14[/latex]

6. [latex]7\left(y-4\right)[/latex]
7. [latex]-3\left(k-4\right)[/latex]
Solution

[latex]-3k+12[/latex]

8. [latex]-8\left(j-5\right)[/latex]
9. [latex]q\left(q+5\right)[/latex]
Solution

[latex]{q}^{2}+5q[/latex]

10. [latex]k\left(k+7\right)[/latex]
11. [latex]-b\left(b+9\right)[/latex]
Solution

[latex]-{b}^{2}-9b[/latex]

12. [latex]-y\left(y+3\right)[/latex]
13. [latex]-x\left(x-10\right)[/latex]
Solution

[latex]-{x}^{2}+10x[/latex]

14. [latex]-p\left(p-15\right)[/latex]
15. [latex]6r\left(4r+s\right)[/latex]
Solution

[latex]24{r}^{2}+6rs[/latex]

16. [latex]5c\left(9c+d\right)[/latex]
17. [latex]12x\left(x-10\right)[/latex]
Solution

[latex]12{x}^{2}-120x[/latex]

18. [latex]9m\left(m-11\right)[/latex]
19. [latex]-9a\left(3a+5\right)[/latex]
Solution

[latex]-27{a}^{2}-45a[/latex]

20. [latex]-4p\left(2p+7\right)[/latex]
21. [latex]3\left({p}^{2}+10p+25\right)[/latex]
Solution

[latex]3{p}^{2}+30p+75[/latex]

22. [latex]6\left({y}^{2}+8y+16\right)[/latex]
23. [latex]-8x\left({x}^{2}+2x-15\right)[/latex]
Solution

[latex]-8{x}^{3}-16{x}^{2}+120x[/latex]

24. [latex]-5t\left({t}^{2}+3t-18\right)[/latex]
25. [latex]5{q}^{3}\left({q}^{3}-2q+6\right)[/latex]
Solution

[latex]5{q}^{6}-10{q}^{4}+30{q}^{3}[/latex]

26. [latex]4{x}^{3}\left({x}^{4}-3x+7\right)[/latex]
27. [latex]-8y\left({y}^{2}+2y-15\right)[/latex]
Solution

[latex]-8{y}^{3}-16{y}^{2}+120y[/latex]

28. [latex]-5m\left({m}^{2}+3m-18\right)[/latex]
29. [latex]5{q}^{3}\left({q}^{2}-2q+6\right)[/latex]
Solution

[latex]5{q}^{5}-10{q}^{4}+30{q}^{3}[/latex]

30. [latex]9{r}^{3}\left({r}^{2}-3r+5\right)[/latex]
31. [latex]-4{z}^{2}\left(3{z}^{2}+12z-1\right)[/latex]
Solution

[latex]-12{z}^{4}-48{z}^{3}+4{z}^{2}[/latex]

32. [latex]-3{x}^{2}\left(7{x}^{2}+10x-1\right)[/latex]
33. [latex]\left(2m-9\right)m[/latex]
Solution

[latex]2{m}^{2}-9m[/latex]


34. [latex]\left(8j-1\right)j[/latex]
35. [latex]\left(w-6\right)\cdot 8[/latex]
Solution

[latex]8w-48[/latex]

36. [latex]\left(k-4\right)\cdot 5[/latex]
37. [latex]4\left(x+10\right)[/latex]
Solution

[latex]4x+40[/latex]

38. [latex]6\left(y+8\right)[/latex]
39. [latex]15\left(r-24\right)[/latex]
Solution

[latex]15r-360[/latex]

40. [latex]12\left(v-30\right)[/latex]
41. [latex]-3\left(m+11\right)[/latex]
Solution

[latex]-3m-33[/latex]

42. [latex]-4\left(p+15\right)[/latex]

43. [latex]-8\left(z-5\right)[/latex]
Solution

[latex]-8z+40[/latex]

44. [latex]-3\left(x-9\right)[/latex]
45. [latex]u\left(u+5\right)[/latex]
Solution

[latex]{u}^{2}+5u[/latex]

46. [latex]q\left(q+7\right)[/latex]
47. [latex]n\left({n}^{2}-3n\right)[/latex]
Solution

[latex]{n}^{3}-3{n}^{2}[/latex]

48. [latex]s\left({s}^{2}-6s\right)[/latex]
49. [latex]6x\left(4x+y\right)[/latex]
Solution

[latex]24{x}^{2}+6xy[/latex]

50. [latex]5a\left(9a+b\right)[/latex]
51. [latex]5p\left(11p-5q\right)[/latex]
Solution

[latex]55{p}^{2}-25pq[/latex]

52. [latex]12u\left(3u-4v\right)[/latex]
53. [latex]3\left({v}^{2}+10v+25\right)[/latex]
Solution

[latex]3{v}^{2}+30v+75[/latex]

54. [latex]6\left({x}^{2}+8x+16\right)[/latex]
55. [latex]2n\left(4{n}^{2}-4n+1\right)[/latex]
Solution

[latex]8{n}^{3}-8{n}^{2}+2n[/latex]

56. [latex]3r\left(2{r}^{2}-6r+2\right)[/latex]
57. [latex]-8y\left({y}^{2}+2y-15\right)[/latex]
Solution

[latex]-8{y}^{3}-16{y}^{2}+120y[/latex]

58. [latex]-5m\left({m}^{2}+3m-18\right)[/latex]
59. [latex]5{q}^{3}\left({q}^{2}-2q+6\right)[/latex]
Solution

[latex]5{q}^{5}-10{q}^{4}+30{q}^{3}[/latex]

60. [latex]9{r}^{3}\left({r}^{2}-3r+5\right)[/latex]
61. [latex]-4{z}^{2}\left(3{z}^{2}+12z-1\right)[/latex]
Solution

[latex]-12{z}^{4}-48{z}^{3}+4{z}^{2}[/latex]

62. [latex]-3{x}^{2}\left(7{x}^{2}+10x-1\right)[/latex]
63. [latex]\left(2y-9\right)y[/latex]
Solution

[latex]18{y}^{2}-9y[/latex]

64. [latex]\left(8b-1\right)b[/latex]

Exercises: Multiply a Binomial by a Binomial

Instructions: For questions 65-68, multiply the following binomials using:

a. the Distributive Property
b. the FOIL method
c. the Vertical Method.

65. [latex]\left(w+5\right)\left(w+7\right)[/latex]
Solution

[latex]{w}^{2}+12w+35[/latex]

66. [latex]\left(y+9\right)\left(y+3\right)[/latex]
67. [latex]\left(p+11\right)\left(p-4\right)[/latex]
Solution

[latex]{p}^{2}+7p-44[/latex]

68. [latex]\left(q+4\right)\left(q-8\right)[/latex]

Exercises: Multiply a Binomial by a Binomial

Instructions: For questions 69-94, multiply the binomials. Use any method.
69. [latex]\left(x+8\right)\left(x+3\right)[/latex]
Solution

[latex]{x}^{2}+11x+24[/latex]

70. [latex]\left(y+7\right)\left(y+4\right)[/latex]
71. [latex]\left(y-6\right)\left(y-2\right)[/latex]
Solution

[latex]{y}^{2}-8y+12[/latex]

72. [latex]\left(x-7\right)\left(x-2\right)[/latex]
73. [latex]\left(w-4\right)\left(w+7\right)[/latex]
Solution

[latex]{w}^{2}+3w-28[/latex]

74. [latex]\left(q-5\right)\left(q+8\right)[/latex]
75. [latex]\left(p+12\right)\left(p-5\right)[/latex]
Solution

[latex]{p}^{2}+7p-60[/latex]

76. [latex]\left(m+11\right)\left(m-4\right)[/latex]
77. [latex]\left(6p+5\right)\left(p+1\right)[/latex]
Solution

[latex]6{p}^{2}+11p+5[/latex]

78. [latex]\left(7m+1\right)\left(m+3\right)[/latex]
79. [latex]\left(2t-9\right)\left(10t+1\right)[/latex]
Solution

[latex]20{t}^{2}-88t-9[/latex]

80. [latex]\left(3r-8\right)\left(11r+1\right)[/latex]
81. [latex]\left(5x-y\right)\left(3x-6\right)[/latex]
Solution

[latex]15{x}^{2}-3xy-30x+6y[/latex]

82. [latex]\left(10a-b\right)\left(3a-4\right)[/latex]
83. [latex]\left(a+b\right)\left(2a+3b\right)[/latex]
Solution

[latex]2{a}^{2}+5ab+3{b}^{2}[/latex]

84. [latex]\left(r+s\right)\left(3r+2s\right)[/latex]
85. [latex]\left(4z-y\right)\left(z-6\right)[/latex]
Solution

[latex]4{z}^{2}-24z-zy+6y[/latex]

86. [latex]\left(5x-y\right)\left(x-4\right)[/latex]
87. [latex]\left({x}^{2}+3\right)\left(x+2\right)[/latex]
Solution

[latex]{x}^{3}+2{x}^{2}+3x+6[/latex]

88. [latex]\left({y}^{2}-4\right)\left(y+3\right)[/latex]
89. [latex]\left({x}^{2}+8\right)\left({x}^{2}-5\right)[/latex]
Solution

[latex]{x}^{4}+3{x}^{2}-40[/latex]

90. [latex]\left({y}^{2}-7\right)\left({y}^{2}-4\right)[/latex]
91. [latex]\left(5ab-1\right)\left(2ab+3\right)[/latex]
Solution

[latex]10{a}^{2}{b}^{2}+13ab-3[/latex]

92. [latex]\left(2xy+3\right)\left(3xy+2\right)[/latex]
93. [latex]\left(6pq-3\right)\left(4pq-5\right)[/latex]
Solution

[latex]24{p}^{2}{q}^{2}-42pq+15[/latex]

94. [latex]\left(3rs-7\right)\left(3rs-4\right)[/latex]

Exercises: Multiply a Trinomial by a Binomial

Instructions: For questions 95-98, multiply using:

a. the Distributive Property
b. the Vertical Method

95. [latex]\left(x+5\right)\left({x}^{2}+4x+3\right)[/latex]
Solution

[latex]{x}^{3}+9{x}^{2}+23x+15[/latex]

96. [latex]\left(u+4\right)\left({u}^{2}+3u+2\right)[/latex]
97. [latex]\left(y+8\right)\left(4{y}^{2}+y-7\right)[/latex]
Solution

[latex]4{y}^{3}+33{y}^{2}+y-56[/latex]

98. [latex]\left(a+10\right)\left(3{a}^{2}+a-5\right)[/latex]

Exercises: Multiply a Trinomial by a Binomial

Instructions: For questions 99-102, multiply. Use either method.
99. [latex]\left(w-7\right)\left({w}^{2}-9w+10\right)[/latex]
Solution

[latex]{w}^{3}-16{w}^{2}+73w-70[/latex]

100. [latex]\left(p-4\right)\left({p}^{2}-6p+9\right)[/latex]
101. [latex]\left(3q+1\right)\left({q}^{2}-4q-5\right)[/latex]
Solution

[latex]3{q}^{3}-11{q}^{2}-19q-5[/latex]

102. [latex]\left(6r+1\right)\left({r}^{2}-7r-9\right)[/latex]

Exercises: Mixed Practice

Instructions: For questions 103-121, solve.

103. [latex]\left(10y-6\right)+\left(4y-7\right)[/latex]
Solution

[latex]14y-13[/latex]

104. [latex]\left(15p-4\right)+\left(3p-5\right)[/latex]
105. [latex]\left({x}^{2}-4x-34\right)-\left({x}^{2}+7x-6\right)[/latex]
Solution

[latex]-11x-28[/latex]

106. [latex]\left({j}^{2}-8j-27\right)-\left({j}^{2}+2j-12\right)[/latex]
107. [latex]5q\left(3{q}^{2}-6q+11\right)[/latex]
Solution

[latex]15{q}^{3}-30{q}^{2}+55q[/latex]

108. [latex]8t\left(2{t}^{2}-5t+6\right)[/latex]
109. [latex]\left(s-7\right)\left(s+9\right)[/latex]
Solution

[latex]{s}^{2}+2s-63[/latex]

110. [latex]\left(x-5\right)\left(x+13\right)[/latex]
111. [latex]\left({y}^{2}-2y\right)\left(y+1\right)[/latex]
Solution

[latex]{y}^{3}-{y}^{2}-2y[/latex]

112. [latex]\left({a}^{2}-3a\right)\left(4a+5\right)[/latex]
113. [latex]\left(3n-4\right)\left({n}^{2}+n-7\right)[/latex]
Solution

[latex]3{n}^{3}-{n}^{2}-25n+28[/latex]

114. [latex]\left(6k-1\right)\left({k}^{2}+2k-4\right)[/latex]
115. [latex]\left(7p+10\right)\left(7p-10\right)[/latex]
Solution

[latex]49{p}^{2}-100[/latex]

116. [latex]\left(3y+8\right)\left(3y-8\right)[/latex]
117. [latex]\left(4{m}^{2}-3m-7\right){m}^{2}[/latex]
Solution

[latex]4{m}^{4}-3{m}^{3}-7{m}^{2}[/latex]

118. [latex]\left(15{c}^{2}-4c+5\right){c}^{4}[/latex]
119. [latex]\left(5a+7b\right)\left(5a+7b\right)[/latex]
Solution

[latex]25{a}^{2}+70ab+49{b}^{2}[/latex]

120. [latex]\left(3x-11y\right)\left(3x-11y\right)[/latex]
121. [latex]\left(4y+12z\right)\left(4y-12z\right)[/latex]
Solution

[latex]16{y}^{2}-144{z}^{2}[/latex]

Exercises: Everyday Math

Instructions: For questions 122-123, solve the given everyday math word problems.

122. Mental math. You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply [latex]13[/latex] times [latex]15[/latex]. Think of [latex]13[/latex] as [latex]10+3[/latex] and [latex]15[/latex] as [latex]10+5[/latex].

a. Multiply [latex]\left(10+3\right)\left(10+5\right)[/latex] by the FOIL method.
b. Multiply [latex]13\cdot 15[/latex] without using a calculator.
c. Which way is easier for you? Why?

123. Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply [latex]18[/latex] times [latex]17[/latex]. Think of [latex]18[/latex] as [latex]20-2[/latex] and [latex]17[/latex] as [latex]20-3[/latex].

a. Multiply [latex]\left(20-2\right)\left(20-3\right)[/latex] by the FOIL method.
b. Multiply [latex]18\cdot 17[/latex] without using a calculator.
c. Which way is easier for you? Why?

Solution

a. [latex]306[/latex]
b. [latex]306[/latex]
c. Answers will vary.

Exercises: Writing Exercises

Instructions: For questions 124-129, answer the given writing exercises.
124. Which method do you prefer to use when multiplying two binomials: the Distributive Property, the FOIL method, or the Vertical Method? Why?
125. Which method do you prefer to use when multiplying a trinomial by a binomial: the Distributive Property or the Vertical Method? Why?
Solution

Answers will vary.

126. Multiply the following:[latex]\begin{array}{c}\left(x+2\right)\left(x-2\right)\\ \left(y+7\right)\left(y-7\right)\\ \left(w+5\right)\left(w-5\right)\end{array}[/latex]

Explain the pattern that you see in your answers.

127. Multiply the following:

[latex]\begin{array}{c}\left(m-3\right)\left(m+3\right)\\ \left(n-10\right)\left(n+10\right)\\ \left(p-8\right)\left(p+8\right)\end{array}[/latex]

Explain the pattern that you see in your answers.

Solution

Answers may vary.

128. Multiply the following:

[latex]\begin{array}{c}\left(p+3\right)\left(p+3\right)\\ \left(q+6\right)\left(q+6\right)\\ \left(r+1\right)\left(r+1\right)\end{array}[/latex]

Explain the pattern that you see in your answers.

129. Multiply the following:

[latex]\begin{array}{c}\left(x-4\right)\left(x-4\right)\\ \left(y-1\right)\left(y-1\right)\\ \left(z-7\right)\left(z-7\right)\end{array}[/latex]

Explain the pattern that you see in your answers.

Solution

Answers may vary.

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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