Which property explains the expansion a(b+c) = ab + ac?

Which property explains the expansion a(b+c) = ab + ac?

• A. Associative Property
• B. Commutative Property
• C. Identity Property
• D. Distributive Property

Answer: (D)

Multiplication distributes over addition: when you multiply a by a sum, you multiply the a by each addend in the sum and then add the results. This is why a(b+c) expands to ab + ac. For example, 3(4+5) = 3·4 + 3·5 = 12 + 15 = 27. Visualize with areas: a rectangle of width a and height (b+c) can be split into two rectangles of areas ab and ac, whose total is ab + ac. This is different from grouping in multiplication (associative), swapping order (commutative), or multiplying by 1 (identity).

Multiplication distributes over addition: when you multiply a by a sum, you multiply the a by each addend in the sum and then add the results. This is why a(b+c) expands to ab + ac. For example, 3(4+5) = 3·4 + 3·5 = 12 + 15 = 27. Visualize with areas: a rectangle of width a and height (b+c) can be split into two rectangles of areas ab and ac, whose total is ab + ac. This is different from grouping in multiplication (associative), swapping order (commutative), or multiplying by 1 (identity).