AI Tutor
Back to Prealgebra 2e

10.3 Multiply Polynomials

Distributing a monomial across a sum, multiplying two binomials by FOIL or a vertical layout, and scaling that method up to a trinomial times a binomial.

Prealgebra 2e, 10.3 Multiply Polynomials

Status
FlagsLoading your progress…

74 exercises

10.3 Exercise 1

Before you get started, take this readiness quiz.

Distribute: 2(x+3).2 \left(x + 3\right) .
If you missed the problem, review the reference.

2.5

10.3 Exercise 2

Distribute: −11(4−3a).−11 \left(4 - 3 a\right) .
If you missed the problem, review the reference.

2.5

10.3 Exercise 3

Combine like terms: x2+9x+7x+63.x^{2} + 9 x + 7 x + 63 .
If you missed the problem, review the reference.

2.5

10.3 Exercise 5

Multiply: 6(x+8).6 \left(x + 8\right) .

2.5

10.3 Exercise 6

Multiply: 2(y+12).2 \left(y + 12\right) .

2.5

10.3 Exercise 8

Multiply: y(y−9).y \left(y - 9\right) .

2.5

10.3 Exercise 9

Multiply: p(p−13).p \left(p - 13\right) .

2.5

10.3 Exercise 11

Multiply: 8x(x+3y).8 x \left(x + 3 y\right) .

2.5

10.3 Exercise 12

Multiply: 3r(6r+s).3 r \left(6 r + s\right) .

2.5

10.3 Exercise 14

Multiply: −4y(8y2+5y−9).−4 y \left(8 y^{2} + 5 y - 9\right) .

2.5

10.3 Exercise 15

Multiply: −6x(9x2+x−1).−6 x \left(9 x^{2} + x - 1\right) .

2.5

10.3 Exercise 17

Multiply: 3x2(4x2−3x+9).3 x^{2} \left(4 x^{2} - 3 x + 9\right) .

2.5

10.3 Exercise 18

Multiply: 8y2(3y2−2y−4).8 y^{2} \left(3 y^{2} - 2 y - 4\right) .

2.5

10.3 Exercise 20

Multiply: (x+8)p.\left(x + 8\right) p .

2.5

10.3 Exercise 21

Multiply: (a+4)p.\left(a + 4\right) p .

2.5

10.3 Exercise 23

Multiply: (x+8)(x+9).\left(x + 8\right) \left(x + 9\right) .

2.5

10.3 Exercise 24

Multiply: (a+4)(a+5).\left(a + 4\right) \left(a + 5\right) .

2.5

10.3 Exercise 26

Multiply: (5x+9)(4x+3).\left(5 x + 9\right) \left(4 x + 3\right) .

2.5

10.3 Exercise 27

Multiply: (10m+9)(8m+7).\left(10 m + 9\right) \left(8 m + 7\right) .

2.5

10.3 Exercise 29

Multiply: (7y+1)(8y−3).\left(7 y + 1\right) \left(8 y - 3\right) .

2.5

10.3 Exercise 30

Multiply: (3x+2)(5x−8).\left(3 x + 2\right) \left(5 x - 8\right) .

2.5

10.3 Exercise 32

Multiply: (x+5)(x−y).\left(x + 5\right) \left(x - y\right) .

2.5

10.3 Exercise 33

Multiply: (x+2y)(x−1).\left(x + 2 y\right) \left(x - 1\right) .

2.5

10.3 Exercise 35

Multiply using the FOIL method: (x+7)(x+8).\left(x + 7\right) \left(x + 8\right) .

2.5

10.3 Exercise 36

Multiply using the FOIL method: (y+14)(y+2).\left(y + 14\right) \left(y + 2\right) .

2.5

10.3 Exercise 38

Multiply: (y−3)(y+8).\left(y - 3\right) \left(y + 8\right) .

2.5

10.3 Exercise 39

Multiply: (q−4)(q+5).\left(q - 4\right) \left(q + 5\right) .

2.5

10.3 Exercise 41

Multiply: (4a+9)(5a−2).\left(4 a + 9\right) \left(5 a - 2\right) .

2.5

10.3 Exercise 42

Multiply: (7x+4)(7x−8).\left(7 x + 4\right) \left(7 x - 8\right) .

2.5

10.3 Exercise 44

Multiply: (12x−y)(x−5).\left(12 x - y\right) \left(x - 5\right) .

2.5

10.3 Exercise 45

Multiply: (6a−b)(2a−9).\left(6 a - b\right) \left(2 a - 9\right) .

2.5

10.3 Exercise 47

Multiply using the vertical method: (4m−9)(3m−7).\left(4 m - 9\right) \left(3 m - 7\right) .

2.5

10.3 Exercise 48

Multiply using the vertical method: (6n−5)(7n−2).\left(6 n - 5\right) \left(7 n - 2\right) .

2.5

10.3 Exercise 50

Multiply using the Distributive Property: (y−1)(y2−7y+2).\left(y - 1\right) \left(y^{2} - 7 y + 2\right) .

2.5

10.3 Exercise 51

Multiply using the Distributive Property: (x+2)(3x2−4x+5).\left(x + 2\right) \left(3 x^{2} - 4 x + 5\right) .

2.5

10.3 Exercise 53

Multiply using the Vertical Method: (y−1)(y2−7y+2).\left(y - 1\right) \left(y^{2} - 7 y + 2\right) .

2.5

10.3 Exercise 54

Multiply using the Vertical Method: (x+2)(3x2−4x+5).\left(x + 2\right) \left(3 x^{2} - 4 x + 5\right) .

2.5

10.3 Exercise 55

Multiply.

4(x+10)4 \left(x + 10\right)

2.5

10.3 Exercise 57

Multiply.

15(r−24)15 \left(r - 24\right)

2.5

10.3 Exercise 59

Multiply.

−3(m+11)−3 \left(m + 11\right)

2.5

10.3 Exercise 61

Multiply.

−8(z−5)−8 \left(z - 5\right)

2.5

10.3 Exercise 63

Multiply.

u(u+5)u \left(u + 5\right)

2.5

10.3 Exercise 65

Multiply.

n(n2−3n)n \left(n^{2} - 3 n\right)

2.5

10.3 Exercise 67

Multiply.

12x(x−10)12 x \left(x - 10\right)

2.5

10.3 Exercise 69

Multiply.

−9a(3a+5)−9 a \left(3 a + 5\right)

2.5

10.3 Exercise 71

Multiply.

6x(4x+y)6 x \left(4 x + y\right)

2.5

10.3 Exercise 73

Multiply.

5p(11p−5q)5 p \left(11 p - 5 q\right)

2.5

10.3 Exercise 75

Multiply.

3(v2+10v+25)3 \left(v^{2} + 10 v + 25\right)

2.5

10.3 Exercise 77

Multiply.

2n(4n2−4n+1)2 n \left(4 n^{2} - 4 n + 1\right)

2.5

10.3 Exercise 79

Multiply.

−8y(y2+2y−15)−8 y \left(y^{2} + 2 y - 15\right)

2.5

10.3 Exercise 81

Multiply.

5q3(q2−2q+6)5 q^{3} \left(q^{2} - 2 q + 6\right)

2.5

10.3 Exercise 83

Multiply.

−4z2(3z2+12z−1)−4 z^{2} \left(3 z^{2} + 12 z - 1\right)

2.5

10.3 Exercise 85

Multiply.

(2y−9)y\left(2 y - 9\right) y

2.5

10.3 Exercise 87

Multiply.

(w−6)·8\left(w - 6\right) \cdot 8

2.5

10.3 Exercise 89

Multiply the following binomials using: ⓐ the Distributive Property ⓑ the FOIL method ⓒ the Vertical method

(x+4)(x+6)\left(x + 4\right) \left(x + 6\right)

2.5

10.3 Exercise 91

Multiply the following binomials using: ⓐ the Distributive Property ⓑ the FOIL method ⓒ the Vertical method

(n+12)(n−3)\left(n + 12\right) \left(n - 3\right)

2.5

10.3 Exercise 93

Multiply the following binomials. Use any method.

(y+8)(y+3)\left(y + 8\right) \left(y + 3\right)

2.5

10.3 Exercise 95

Multiply the following binomials. Use any method.

(a+6)(a+16)\left(a + 6\right) \left(a + 16\right)

2.5

10.3 Exercise 97

Multiply the following binomials. Use any method.

(u−5)(u−9)\left(u - 5\right) \left(u - 9\right)

2.5

10.3 Exercise 99

Multiply the following binomials. Use any method.

(z−10)(z−22)\left(z - 10\right) \left(z - 22\right)

2.5

10.3 Exercise 101

Multiply the following binomials. Use any method.

(x−4)(x+7)\left(x - 4\right) \left(x + 7\right)

2.5

10.3 Exercise 103

Multiply the following binomials. Use any method.

(v+12)(v−5)\left(v + 12\right) \left(v - 5\right)

2.5

10.3 Exercise 105

Multiply the following binomials. Use any method.

(6n+5)(n+1)\left(6 n + 5\right) \left(n + 1\right)

2.5

10.3 Exercise 107

Multiply the following binomials. Use any method.

(2m−9)(10m+1)\left(2 m - 9\right) \left(10 m + 1\right)

2.5

10.3 Exercise 109

Multiply the following binomials. Use any method.

(4c−1)(4c+1)\left(4 c - 1\right) \left(4 c + 1\right)

2.5

10.3 Exercise 111

Multiply the following binomials. Use any method.

(3u−8)(5u−14)\left(3 u - 8\right) \left(5 u - 14\right)

2.5

10.3 Exercise 113

Multiply the following binomials. Use any method.

(a+b)(2a+3b)\left(a + b\right) \left(2 a + 3 b\right)

2.5

10.3 Exercise 115

Multiply the following binomials. Use any method.

(5x−y)(x−4)\left(5 x - y\right) \left(x - 4\right)

2.5

10.3 Exercise 117

Multiply using ⓐ the Distributive Property and ⓑ the Vertical Method.

(u+4)(u2+3u+2)\left(u + 4\right) \left(u^{2} + 3 u + 2\right)

2.5

10.3 Exercise 119

Multiply using ⓐ the Distributive Property and ⓑ the Vertical Method.

(a+10)(3a2+a−5)\left(a + 10\right) \left(3 a^{2} + a - 5\right)

2.5

10.3 Exercise 121

Multiply. Use either method.

(y−6)(y2−10y+9)\left(y - 6\right) \left(y^{2} - 10 y + 9\right)

2.5

10.3 Exercise 123

Multiply. Use either method.

(2x+1)(x2−5x−6)\left(2 x + 1\right) \left(x^{2} - 5 x - 6\right)

2.5

10.3 Exercise 125

Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 1313 times 15.15 . Think of 1313 as 10+310 + 3 and 1515 as 10+5.10 + 5 .

  1. ⓐ Multiply (10+3)(10+5)\left(10 + 3\right) \left(10 + 5\right) by the FOIL method.
  2. ⓑ Multiply 13·1513 \cdot 15 without using a calculator.
  3. ⓒ Which way is easier for you? Why?
2.5

10.3 Exercise 127

Which method do you prefer to use when multiplying two binomials—the Distributive Property, the FOIL method, or the Vertical Method? Why?

2.5

Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.