Which numeric expression illustrates the distributive property?

Which numeric expression illustrates the distributive property?

• A. 3(2 + 5) = 6 + 15
• B. (a + b) + c = a + (b + c)
• C. 9h = 3h × 3
• D. 7 + 4 = 4 + 7

Answer: (A)

The distributive property says that multiplying a number outside the parentheses by a sum inside distributes to each addend, so a(b+c) = ab + ac. For 3(2+5), distribute the 3 to both 2 and 5: 3×2 + 3×5 = 6 + 15. Since 3(2+5) also equals 21, both sides match, illustrating the property. The other forms show different ideas—rearranging addition (associative), swapping the order of addends (commutative), or a straightforward multiplication fact—none of which demonstrate distributing a factor across a sum.

The distributive property says that multiplying a number outside the parentheses by a sum inside distributes to each addend, so a(b+c) = ab + ac. For 3(2+5), distribute the 3 to both 2 and 5: 3×2 + 3×5 = 6 + 15. Since 3(2+5) also equals 21, both sides match, illustrating the property. The other forms show different ideas—rearranging addition (associative), swapping the order of addends (commutative), or a straightforward multiplication fact—none of which demonstrate distributing a factor across a sum.