Which equation shows the distributive property over subtraction?

Which equation shows the distributive property over subtraction?

• A. A × (B - C) = A × B - A × C
• B. A × (B - C) = A × B + A × C
• C. A × B - C = (A × B) - C
• D. A × B + C = A × (B - C)

Answer: (A)

Distributing multiplication across a subtraction means applying the outside factor to each term inside the parentheses, keeping the subtraction sign as subtraction of the second product. So you multiply A by B and by C, but the second product is subtracted. That gives A × (B − C) = A × B − A × C. For example, with A = 3, B = 5, C = 2: both sides become 3 × (5 − 2) = 3 × 3 = 9, and 3 × 5 − 3 × 2 = 15 − 6 = 9, confirming the rule. The other forms don’t represent distributing over subtraction: using addition inside the distribution would yield A × (B − C) = A × B + A × C, which is not correct for subtraction; A × B − C or A × B + C ignore distributing A over both terms inside the parentheses, so they don’t match the distributive process.

Distributing multiplication across a subtraction means applying the outside factor to each term inside the parentheses, keeping the subtraction sign as subtraction of the second product. So you multiply A by B and by C, but the second product is subtracted. That gives A × (B − C) = A × B − A × C.

For example, with A = 3, B = 5, C = 2: both sides become 3 × (5 − 2) = 3 × 3 = 9, and 3 × 5 − 3 × 2 = 15 − 6 = 9, confirming the rule.

The other forms don’t represent distributing over subtraction: using addition inside the distribution would yield A × (B − C) = A × B + A × C, which is not correct for subtraction; A × B − C or A × B + C ignore distributing A over both terms inside the parentheses, so they don’t match the distributive process.