Which expression demonstrates the distributive property?

• A. a(b + c) = ab + ac
• B. a(b + c) = ab + c
• C. (a + b)c = ac + bc
• D. a + b = b + a

Answer: (A)

Distributive property means you multiply a factor through a sum by multiplying it with each addend separately and then adding the results. So a(b + c) expands to ab + ac. This directly matches the rule: the single factor multiplies both terms inside the parentheses, producing two products that are added together. For example, 2(5 + 7) becomes 2×5 + 2×7, which is 10 + 14.

The other forms don’t illustrate this process in the same way: one option would drop a factor and isn’t a correct expansion, another is just the addition of terms without any multiplication, and a different form places the multiplication on the other side of the sum. The expression shown, with the multiplier outside and the sum inside, clearly demonstrates distributing the product over addition.