Distribution, Subtraction, and Factoring Practice — Grade 4 amc_math

Lesson 3: Distribution, Subtraction, and Factoring — Practice Questions

1. Simplify the expression: $(5a + 8) - (2a + 3)$. The simplified expression is ___.
2. What is the result of subtracting $(3b - 2)$ from $(7b + 4)$?
- A. 4b + 6
- B. 4b + 2
- C. 10b + 2
- D. 10b + 6
3. Simplify the expression $(6m - 5) - (m - 9)$. The result is ___.
4. Which expression is equivalent to $(8k + 1) - (4k + 5)$ after distributing the negative sign?
- A. 8k + 1 - 4k - 5
- B. 8k + 1 - 4k + 5
- C. 8k + 1 + 4k + 5
- D. 8k + 1 + 4k - 5
5. Subtract $(3x + 9)$ from $(2 - 5x)$. The simplified result is ___.
6. Factor the expression completely: $9(z - 5) + 2(z - 5)$. The result can be written as $11(\_\_\_)$.
7. Which expression is equivalent to $y(p + q) - 8(p + q)$?
- A. (p + q)(y - 8)
- B. (p + q)(y + 8)
- C. (p - q)(y - 8)
- D. -8y(p + q)
8. Factor the expression $5m(2n - 3) + 6(2n - 3)$. The result is $(2n - 3)(\_\_\_)$.
9. Which expression is the correctly factored form of $x(y - 4) + 6(y - 4)$?
- A. (x + 6)(y - 4)
- B. (x - 6)(y + 4)
- C. 6x(y - 4)
- D. (x + y)(6 - 4)
10. Factor the expression completely: $7(a - b) - c(a - b) = (a - b)(\_\_\_)$.