Which expression correctly shows the Distributive Property: a(b + c) = ab + ac?

Which expression correctly shows the Distributive Property: a(b + c) = ab + ac?

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

Answer: (D)

The distributive property means you multiply the outside factor by each term inside the parentheses and then add the results. So a times (b plus c) distributes to ab plus ac, written as a(b+c) = ab + ac. For a quick check with numbers: 3(5+2) = 3·5 + 3·2 = 15 + 6 = 21. This shows exactly how the outside factor multiplies each inside term and the results are added. The other forms would imply a different inside operation or misplace the addition, so they don’t match the rule for distributing over a sum.

The distributive property means you multiply the outside factor by each term inside the parentheses and then add the results. So a times (b plus c) distributes to ab plus ac, written as a(b+c) = ab + ac.

For a quick check with numbers: 3(5+2) = 3·5 + 3·2 = 15 + 6 = 21. This shows exactly how the outside factor multiplies each inside term and the results are added.

The other forms would imply a different inside operation or misplace the addition, so they don’t match the rule for distributing over a sum.