➕ Algebra 1 · Equations

The Distributive Property practice questions

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Answer key with explanations

1. Expand 10(x + 4).

   Answer: 10x + 40. The 10 multiplies both terms: 10 × x = 10x and 10 × 4 = 40, so the answer is 10x + 40.

2. Expand 4(3y − 5).

   Answer: 12y − 20. Think of 3y − 5 as 3y + (−5). Then 4 × 3y = 12y and 4 × (−5) = −20, so the answer is 12y − 20.

3. Expand −6(5 − 2x).

   Answer: 12x − 30. The terms inside are 5 and −2x. Then (−6) × 5 = −30 and (−6) × (−2x) = +12x. That gives −30 + 12x, which is the same as 12x − 30.

4. Factor the greatest common factor out of 14x + 21.

   Answer: 7(2x + 3). Both 14 and 21 are divisible by 7, and 7 is the largest number that works for both. Then 14x ÷ 7 = 2x and 21 ÷ 7 = 3, so the answer is 7(2x + 3). Check: 7 × 2x + 7 × 3 = 14x + 21.

5. Which shows a correct way to find 9 × 62 with the distributive property?

   Answer: 9(60 + 2) = 540 + 18 = 558. Split 62 into 60 + 2 and multiply each part by 9: 9 × 60 = 540 and 9 × 2 = 18. Then add: 540 + 18 = 558. The other choices skip the 9 on the second part, multiply the parts instead of adding them, or add where the minus sign belongs (630 − 72 = 558).

6. Expand and simplify 5 + 3(x − 4).

   Answer: 3x − 7. Only the 3 multiplies the parentheses: 3(x − 4) = 3x − 12. The 5 is added afterward: 5 + 3x − 12 = 3x − 7. Adding 5 + 3 first, as in 8(x − 4), breaks the order of operations.

7. Expand (2/3)(9x − 12).

   Answer: 6x − 8. Multiply each term by 2/3: (2/3)(9x) = 6x and (2/3)(−12) = −8. So the answer is 6x − 8.

8. Four friends each buy a movie ticket that costs t dollars and a drink that costs 3 dollars. Which expression gives their total cost in dollars?

   Answer: 4t + 12. Each friend pays t + 3 dollars, and there are 4 friends, so the total is 4(t + 3). Distributing gives 4t + 12. The 4 has to multiply the drink’s cost too.