What is the distributive property?

What is the distributive property?

• A. A (B+C) = AB + AC
• B. A + B = B + A
• C. A(B+C) = AB + CB
• D. A(B−C) = AB − CB

Answer: (A)

Distributive property means multiplying a single factor outside the parentheses by each term inside the parentheses, then adding the results. In algebra, this is written as a(b + c) = ab + ac. That is exactly the idea shown by the correct form: multiply the outside factor with each term inside the sum and then add. For a concrete check, 3(4 + 5) = 3×4 + 3×5 = 12 + 15 = 27. The other ideas are different properties or forms. Adding with no regard to the parentheses (a + b = b + a) is the commutative property of addition, not distributing. And distributing over subtraction would give a(b − c) = ab − ac, not ab − cb, so that form isn’t the distributive pattern.

Distributive property means multiplying a single factor outside the parentheses by each term inside the parentheses, then adding the results. In algebra, this is written as a(b + c) = ab + ac. That is exactly the idea shown by the correct form: multiply the outside factor with each term inside the sum and then add. For a concrete check, 3(4 + 5) = 3×4 + 3×5 = 12 + 15 = 27.

The other ideas are different properties or forms. Adding with no regard to the parentheses (a + b = b + a) is the commutative property of addition, not distributing. And distributing over subtraction would give a(b − c) = ab − ac, not ab − cb, so that form isn’t the distributive pattern.