Which expression demonstrates the distributive property of multiplication over addition?

Which expression demonstrates the distributive property of multiplication over addition?

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

Answer: (B)

The distributive property says that multiplying a factor outside the parentheses across a sum inside the parentheses distributes to each addend. The expression a(b + c) = ab + ac is exactly that rule: multiply a by b and by c, then add the results. For a concrete check, take a = 3, b = 4, c = 5: 3(4 + 5) = 3(9) = 27, and 3·4 + 3·5 = 12 + 15 = 27. This confirms the distribution. The other patterns are different properties: ac = bc isn’t a general rule (it would force a = b if c ≠ 0), a + b = b + a is the commutative property of addition, and (a + b) + c = a + (b + c) is the associative property of addition.

The distributive property says that multiplying a factor outside the parentheses across a sum inside the parentheses distributes to each addend. The expression a(b + c) = ab + ac is exactly that rule: multiply a by b and by c, then add the results. For a concrete check, take a = 3, b = 4, c = 5: 3(4 + 5) = 3(9) = 27, and 3·4 + 3·5 = 12 + 15 = 27. This confirms the distribution. The other patterns are different properties: ac = bc isn’t a general rule (it would force a = b if c ≠ 0), a + b = b + a is the commutative property of addition, and (a + b) + c = a + (b + c) is the associative property of addition.