Which property explains that a × (b + c) = ab + ac?

• A. Distributive Property
• B. Associative Property of Addition
• C. Commutative Property of Multiplication
• D. Identity Property

Answer: (A)

This is about the distributive property: when you multiply a number by a sum, you can multiply by each addend and then add the products. In symbols, a × (b + c) equals ab + ac because the multiplication “distributes” across the addition.

For a concrete check, use numbers: 3 × (4 + 5) equals 3 × 9, which is 27. If you distribute first, you get 3 × 4 + 3 × 5, which is 12 + 15, also 27. So both paths give the same result.

This property is what lets us expand expressions like ab + ac from a(b + c). The other properties don’t describe this kind of spreading of multiplication over addition: the associative property of addition only groups addends, the commutative property rearranges order, and the identity properties involve multiplying by 1 or adding 0.