Quiz Answers with Explanations

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I can: expand expressions using the distributive property and FOIL.

Success criteria: Apply distributive property correctly, combine like terms, and check by substitution.

Differentiation: Read aloud, use a ruler or colored overlay, expand one term at a time. Extension: expand a trinomial product.

📚 Part 1: Multiple Choice & Review

1. Expand 3(x + 4).

3x + 4

3x + 12

x + 12

9x + 12

Answer: 3x + 12. Explanation: Use the distributive property: 3·x + 3·4 = 3x + 12.

2. Expand -2(3x - 5).

-6x + 10

-6x - 10

6x + 10

6x - 10

Answer: -6x + 10. Explanation: Multiply each term by -2: -2·3x = -6x and -2·(-5) = +10.

3. Expand (x + 6)(x - 2).

x^2 + 4x - 12

x^2 + 8x - 12

x^2 + 4x + 12

x^2 - 4x - 12

Answer: x^2 + 4x - 12. Explanation: FOIL: x·x = x^2, x·(-2) = -2x, 6·x = 6x, 6·(-2) = -12. Combine -2x + 6x = 4x.

4. Check all that apply: Which are equivalent to 2(x + 3)?

2x + 6

x + 6

4x + 6

2x + 3 + 3

Answers: 2x + 6 and 2x + 3 + 3. Explanation: 2(x+3) = 2x + 6. The expression 2x + 3 + 3 simplifies to 2x + 6 as well. x + 6 and 4x + 6 are not equivalent.

✏️ Part 2: Short Answers

5. Expand and simplify: 5(2x + 3).

5·2x + 5·3 = 10x + 15

Answer: 10x + 15. Explanation: Distribute 5 to each term inside the parentheses.

6. Expand: (2x - 1)(x + 4). Show your steps.

FOIL: 2x·x + 2x·4 + (-1)·x + (-1)·4 = 2x^2 + 8x - x - 4 = 2x^2 + 7x - 4

Answer: 2x^2 + 7x - 4. Explanation: Multiply each pair of terms, then combine like terms (8x - x = 7x).

7. Expand and combine like terms: 4x(x + 2) - 3(x + 5).

4x·x + 4x·2 - 3·x - 3·5 = 4x^2 + 8x - 3x - 15 = 4x^2 + 5x - 15

Answer: 4x^2 + 5x - 15. Explanation: Distribute each factor, then combine 8x and -3x.

8. Word problem: A ribbon has length 3x + 2 inches. It is cut into 4 equal pieces. Write an expression for one piece and then expand or simplify it.

One piece = (3x + 2) ÷ 4 = (1/4)(3x + 2) = 3/4·x + 2/4 = (3/4)x + 1/2

Answer: (3/4)x + 1/2. Explanation: Divide each term by 4 to split the ribbon equally.

Extension (optional):

Create and expand a trinomial product, for example (x + 2)(x - 1)(x + 3). Try expanding two at a time, then multiply the result by the third factor.

Quiz Answers with Explanations

Quiz Answers with Explanations

📚 Part 1: Multiple Choice & Review

✏️ Part 2: Short Answers

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