By LearningExpress Editors
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.
- (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) = x^{2} | |
Outside: (x)(3) = 3x | |
Inside: (2)(x) = 2x | |
Last: (2)(3) = 6 | |
x^{2} + 3x + 2x + 6 = x^{2} + 5x + 6 | |
2. | Use FOIL and combine like terms: |
First: (2x)(x) = 2x^{2} | |
Outside: (2x)(5) = –10x | |
inside: (–1)(x) = –x | |
Last: (–1)(–5) = 5 | |
2x^{2} – 10x – x + 5 = 2x^{2} – 11x + 5 | |
3. | Use FOIL and combine like terms: |
First: (3x)(6x) = 18x^{2} | |
Outside:(3x)(–10) = –30x | |
Inside: (7)(6x) = 42x | |
Last: (7)(–10) = –70 | |
18x^{2} – 30x + 42x – 70 = 18x^{2} + 12x – 70 | |
4. | Use FOIL and combine like terms: |
First:(–x)(8x) = –8x^{2} | |
Outside: (–x)(15) = –15x | |
Inside: (3)(8x) = 24x | |
Last: (3)(15) = 45 | |
–8x^{2} – 15x + 24x + 45 = – 8x^{2} + 9x + 45 | |
5. | Use FOIL and combine like terms: |
First: (7x)(2x) = 14x^{2} | |
Outside: (7x)(4) = 28x | |
Inside: (2)(2x) = 4x | |
Last: (2)(4) = 8 | |
14x^{2} + 28x + 4x + 8 = 14x^{2} + 32x + 8 | |
6. | Use FOIL and combine like terms: |
First: (x)(9x) = 9x^{2} | |
Outside: (x)(–8) = –8x | |
Inside: (9)(9x) = 81x | |
Last: (9)(–8) = 72 | |
9x^{2} – 8x + 81x – 72 = 9x^{2} + 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) = x^{2} | |
Outside: (x)(–8) = –8x | |
Inside: (–8)(x) = –8x | |
Last: (–8)(–8) = 64 | |
x^{2} – 8x – 8x + 64 = x^{2} – 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) = 9x^{2} | |
Outside: (3x)(2) = 6x | |
Inside: (2)(3x) = 6x | |
Last: (2)(2) = 4 | |
9x^{2} + 6x + 6x + 4 = 9x^{2} + 12x + 4 | |
9. | Use FOIL and combine like terms: |
First: (x)(x) = x^{2} | |
Outside: (x)(–10) = –10x | |
inside: (10)(x) = 10x | |
Last: (10)(–10) = –100 | |
x^{2} – 10x + 10x – 100 = x^{2} – 100 | |
10. | Use FOIL and combine like terms: |
First: (5x)(5x) = 25x^{2} | |
Outside: (5x)(12) = 60x | |
Inside: (–12)(5x) = –60x | |
Last: (–12)(12) = –144 | |
25x^{2} + 60x – 60x – 144 = 25x^{2} – 144 |
From Algebra in 15 Minutues A Day. Copyright © 2009 by LearningExpress, LLC. All Rights Reserved.
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