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.
- (x + 2)(x + 3)
- (2x –1)(x –5)
- (3x + 7)(6x – 10)
- (–x + 3)(8x + 15)
- (7x + 2)(2x + 4)
- (x + 9)(9x –8)
- (x – 8)2
- (3x + 2)2
- (x + 10)(x – 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 |
Excerpted From:
From Algebra in 15 Minutues A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.
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