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Year 9 Mathematics · Expanding binomial products

Name: ______________________

Date: ____________

1. Expand and simplify (x + 2)(x + 4).
- ☐ (a) x^2 + 8x + 6
- ☐ (b) x^2 + 6x + 8
- ☐ (c) x^2 + 8
- ☐ (d) x^2 + 6x + 6
2. Expand and simplify (x − 3)(x + 7).
- ☐ (a) x^2 − 4x − 21
- ☐ (b) x^2 + 4x + 21
- ☐ (c) x^2 + 4x − 21
- ☐ (d) x^2 − 21
3. Expand (x + 5)^2.
- ☐ (a) x^2 + 10x + 25
- ☐ (b) x^2 + 25
- ☐ (c) x^2 + 5x + 25
- ☐ (d) 2x + 10
4. Expand (x − 4)(x + 4).
- ☐ (a) x^2 − 8x − 16
- ☐ (b) x^2 + 16
- ☐ (c) x^2 − 8
- ☐ (d) x^2 − 16
5. Expand and simplify (3x + 2)(x − 1).
- ☐ (a) 3x^2 + x − 2
- ☐ (b) 3x^2 − x − 2
- ☐ (c) 3x^2 − 5x − 2
- ☐ (d) 4x^2 − x − 2
6. When (x + 9)(x − 2) is expanded and simplified, what is the coefficient of x?
7. When (x − 6)(x − 8) is expanded, what is the constant term (the term with no x)?
8. When (2x + 5)^2 is expanded and simplified, what is the coefficient of x?

Answer sheet

1. x^2 + 6x + 8 — The products are x^2, 4x, 2x and 8. Collecting like terms gives x^2 + 6x + 8.
2. x^2 + 4x − 21 — The products are x^2, 7x, −3x and −21. Since 7x − 3x = 4x, the answer is x^2 + 4x − 21.
3. x^2 + 10x + 25 — (x + 5)(x + 5) gives x^2 + 5x + 5x + 25 = x^2 + 10x + 25.
4. x^2 − 16 — This is a difference of two squares. The middle terms −4x and +4x cancel, leaving x^2 − 16.
5. 3x^2 − x − 2 — The products are 3x^2, −3x, 2x and −2. Since −3x + 2x = −x, the answer is 3x^2 − x − 2.
6. 7 — The x terms are −2x and 9x, which add to 7x. So the coefficient is 7.
7. 48 — The constant term is (−6) × (−8) = 48. A negative times a negative is positive.
8. 20 — (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25, so the coefficient of x is 20.