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.

Examples 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

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 - . . .
  

Solved Example on Distributive Property

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.                                                           

Related Terms for Distributive Property

• Sum
• Product
• Addend

Additional Links for Distributive Property

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