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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
a(b + c) = ab + ac is known as left distributive
(b + c)a = ba + ca is known as right distributive

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 x 3 + 5 x 1
Consider LHS: 5(3 + 1) = 5(4) = 20
Consider RHS: 5 x 3 + 5 x 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 x 5 + 2 x 2 = 10 + 4 = 14
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