Which equation shows the distributive property of multiplication over addition?

Which equation shows the distributive property of multiplication over addition?

• 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)

The distributive property means multiplying a number by a sum distributes to multiply the number by each addend and then add those products. In symbols, a × (b + c) equals a × b + a × c. This is exactly the form shown when you multiply across both parts of the sum and then add the results. For example, using a = 2, b = 3, c = 4: 2 × (3 + 4) = 2 × 7 = 14, and 2 × 3 + 2 × 4 = 6 + 8 = 14. The two sides match, illustrating the distributive property. The other expressions don’t follow this rule: using subtraction inside the parentheses would change the operation to a × (b + c) = a × b − a × c, which isn’t correct because you’re not subtracting the second product. Expanding the left side to a × b + c would imply that c equals a × c, which is not generally true. Expanding to a × b + c omits the second product entirely, so you don’t account for multiplying a by the other addend. Thus, the correct form is the one that distributes the multiplier to both addends.

The distributive property means multiplying a number by a sum distributes to multiply the number by each addend and then add those products. In symbols, a × (b + c) equals a × b + a × c. This is exactly the form shown when you multiply across both parts of the sum and then add the results.

For example, using a = 2, b = 3, c = 4: 2 × (3 + 4) = 2 × 7 = 14, and 2 × 3 + 2 × 4 = 6 + 8 = 14. The two sides match, illustrating the distributive property.

The other expressions don’t follow this rule: using subtraction inside the parentheses would change the operation to a × (b + c) = a × b − a × c, which isn’t correct because you’re not subtracting the second product. Expanding the left side to a × b + c would imply that c equals a × c, which is not generally true. Expanding to a × b + c omits the second product entirely, so you don’t account for multiplying a by the other addend. Thus, the correct form is the one that distributes the multiplier to both addends.