Distributive Property

Definition of Distributive Property

Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number.
That is, a(b + c) = ab + ac.

More About Distributive Property

    The property is true for any number of addends.
    That is, a(b + c + d + . . . .) = ab + ac + ad + . . . . .
    Also,
    a(b - c) = ab - ac and a (b - c - d - . . . ) = ab - ac - ad - . . .

Example of Distributive Property

    5(3 + 1) = 5 3 + 5 1
    Consider LHS: 5(3 + 1) = 5(4) = 20
    Consider RHS: 5 3 + 5 1 = 15 + 5 = 20
    LHS = RHS

Video Examples: The Distributive Property


Solved Example on Distributive Property

Ques: Using the distributive property, evaluate x(y + 2), for x = 2 and y = 5.

    Choices:
    A. 14
    B. 12
    C. 20
    D. 9
    Correct Answer: A

Solution:

    Step 1: x(y + 2) = xy + 2x, using the distributive property.
    Step 2: Substitute the values of x and y in the expression.
    Step 3: = 2 5 + 2 2 = 10 + 4 = 14.