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# Polynomials and Multiplying Binomials Practice Questions

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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 – 10x – x + 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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