Which expression demonstrates the associative property of multiplication?

Which expression demonstrates the associative property of multiplication?

• A. (ab)c = a(bc)
• B. a + b = b + a
• C. a(b + c) = ab + ac
• D. y - y1 = m(x - x1)

Answer: (A)

Associative property of multiplication means that how you group factors doesn't change the product. The expression (ab)c = a(bc) shows this directly: multiply a and b first, then multiply by c, or multiply b and c first, then multiply by a, and you still get the same result (abc). This equality demonstrates that the product of three numbers is unaffected by how you group them. The other options illustrate different ideas: adding is shown as a + b = b + a (commutativity of addition), a(b + c) = ab + ac displays the distributive property, and y - y1 = m(x - x1) is a line's point-slope form, not a property of multiplying factors.

Associative property of multiplication means that how you group factors doesn't change the product. The expression (ab)c = a(bc) shows this directly: multiply a and b first, then multiply by c, or multiply b and c first, then multiply by a, and you still get the same result (abc). This equality demonstrates that the product of three numbers is unaffected by how you group them. The other options illustrate different ideas: adding is shown as a + b = b + a (commutativity of addition), a(b + c) = ab + ac displays the distributive property, and y - y1 = m(x - x1) is a line's point-slope form, not a property of multiplying factors.