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Polynomials and Multiplying Binomials Practice Questions

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Updated on Oct 9, 2013

To review these concepts, go to Polynomials and Multiplying Binomials Study Guide.

Polynomials and Multiplying Binomials Practice Questions

Practice

Find the product of each binomial.

  1. (x + 2)(x + 3)
  2. (2x –1)(x –5)
  3. (3x + 7)(6x – 10)
  4. (–x + 3)(8x + 15)
  5. (7x + 2)(2x + 4)
  6. (x + 9)(9x –8)
  7. (x – 8)2
  8. (3x + 2)2
  9. (x + 10)(x – 10)
  10. (5x – 12)(5x + 12)

Solutions

1. Use FOIL and combine like terms:
First: (x)(x) = x2
Outside: (x)(3) = 3x
Inside: (2)(x) = 2x
Last: (2)(3) = 6
x2 + 3x + 2x + 6 = x2 + 5x + 6
2. Use FOIL and combine like terms:
First: (2x)(x) = 2x2
Outside: (2x)(5) = –10x
inside: (–1)(x) = –x
Last: (–1)(–5) = 5
2x2 – 10xx + 5 = 2x2 – 11x + 5
3. Use FOIL and combine like terms:
First: (3x)(6x) = 18x2
Outside:(3x)(–10) = –30x
Inside: (7)(6x) = 42x
Last: (7)(–10) = –70
18x2 – 30x + 42x – 70 = 18x2 + 12x – 70
4. Use FOIL and combine like terms:
First:(–x)(8x) = –8x2
Outside: (–x)(15) = –15x
Inside: (3)(8x) = 24x
Last: (3)(15) = 45
–8x2 – 15x + 24x + 45 = – 8x2 + 9x + 45
5. Use FOIL and combine like terms:
First: (7x)(2x) = 14x2
Outside: (7x)(4) = 28x
Inside: (2)(2x) = 4x
Last: (2)(4) = 8
14x2 + 28x + 4x + 8 = 14x2 + 32x + 8
6. Use FOIL and combine like terms:
First: (x)(9x) = 9x2
Outside: (x)(–8) = –8x
Inside: (9)(9x) = 81x
Last: (9)(–8) = 72
9x2 – 8x + 81x – 72 = 9x2 + 73x – 72
7. Because (x –8) is raised to the second power, multiply it by itself: (x –8)2 = (x –8)(x –8). Use FOIL and combine like terms:
First: (x)(x) = x2
Outside: (x)(–8) = –8x
Inside: (–8)(x) = –8x
Last: (–8)(–8) = 64
x2 – 8x – 8x + 64 = x2 – 16x+ 64
8. Because (3x + 2) is raised to the second power, multiply it by itself: (3x + 2)2 = (3x + 2)(3x + 2). Use FOIL and combine like terms:
First: (3x)(3x) = 9x2
Outside: (3x)(2) = 6x
Inside: (2)(3x) = 6x
Last: (2)(2) = 4
9x2 + 6x + 6x + 4 = 9x2 + 12x + 4
9. Use FOIL and combine like terms:
First: (x)(x) = x2
Outside: (x)(–10) = –10x
inside: (10)(x) = 10x
Last: (10)(–10) = –100
x2 – 10x + 10x – 100 = x2 – 100
10. Use FOIL and combine like terms:
First: (5x)(5x) = 25x2
Outside: (5x)(12) = 60x
Inside: (–12)(5x) = –60x
Last: (–12)(12) = –144
25x2 + 60x – 60x – 144 = 25x2 – 144
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