➕ Algebra 1 · Equations

The Distributive Property: true or false

Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.

All statements and answers

• The property also works when the parentheses come first: (x + 4) × 3 = 3x + 12.

  ✓ True. Multiplication can be done in either order. The 3 still multiplies both the x and the 4.

• 6(x + 5) = 6x + 5.

  ✗ False. The 6 must multiply the 5 as well: 6(x + 5) = 6x + 30. Check with x = 3: 6(3 + 5) = 48, but 6(3) + 5 = 23.

• −4(x − 3) = −4x − 12.

  ✗ False. The second term is −3, and (−4) × (−3) = +12, so the answer is −4x + 12. Check with x = 4: −4(4 − 3) = −4, and −4(4) + 12 = −4, but −4(4) − 12 = −28.

• −(5 − x) equals x − 5.

  ✓ True. The minus sign flips both signs inside: −5 + x, which is the same as x − 5.

• (x + 4)² = x² + 16.

  ✗ False. An exponent does not distribute over a sum. Try x = 3: (3 + 4)² = 49, but 3² + 16 = 25.

• 10x + 25 = 5(2x + 5).

  ✓ True. Distributing the 5 gives 5 × 2x + 5 × 5 = 10x + 25, so this is a correct factoring. The 5 is the greatest common factor of 10 and 25.

• 30 ÷ (3 + 2) equals 30 ÷ 3 + 30 ÷ 2.

  ✗ False. The left side is 30 ÷ 5 = 6. The right side is 10 + 15 = 25. Dividing a number by a sum does not distribute. (Dividing a sum by a number does.)

• (8x + 12) ÷ 4 = 2x + 3.

  ✓ True. Dividing a sum by a number divides each term: 8x ÷ 4 = 2x and 12 ÷ 4 = 3.

• 7 + 3(x + 2) = 10x + 20.

  ✗ False. Multiplication comes before addition, and the 3 multiplies only the parentheses: 7 + 3x + 6 = 3x + 13. Check with x = 3: 7 + 3(3 + 2) = 22 and 3(3) + 13 = 22, but 10(3) + 20 = 50.

• 5 × 12 = 5 × 10 + 5 × 2 is an example of the distributive property.

  ✓ True. Splitting 12 into 10 + 2 and multiplying each part by 5 gives 50 + 10 = 60, the same as 5 × 12.