Distributive Law to Factor

In mathematics, factor is one of the important topics in algebra. Factor is the process of performing multiplication in reverse. Distributive law is the process of the product of a terms and a sum is equal to the sum of the individual products of the addends and the terms. Let us solve some example problems for factor using the distributive law.

Distributive property:

a . (b + c) = ab + ac

Distributive Law to Factor - Steps:

Different steps to solve the factor using distributive law are

  • Given expression
  • For each term in the expression can determine the greatest common factor.
  • Each term can be divided by the greatest common factor
  • Product of the greatest common factor and the remaining factor of the each term can be written as distributive law.
  • Solution to the given expression

Distributive Law to Factor - Example Problems:

Example 1:

Factor the given expression

18a2b5 + 6ab2 + 24ab

Solution:

Given expression

18a2b5 + 6ab2 + 24ab

Factor the each term

First term in the expression can be factored

18a2b5 = 2 . 3 . 3 . a . a . b . b . b . b . b

Second term in the expression can be factored

6ab2 = 2 . 3 . a . b . b

Last term in the expression can be factored

24ab = 2 . 2 . 2 . 3 . a . b

Determine the greatest common factor for the expression 6ab

Using the distributive law the expression can be written as

18a2b5 + 6ab2 + 24ab = 6ab (3ab4) + 6ab (b) + 6ab (4)

                                   = 6ab (3ab4 + b + 4)

Answer:

18a2b5 + 6ab2 + 24ab = 6ab (3ab4 + b + 4)

Example 2:

Factor the given expression

20a3b4 + 25a2b2 + 10a5b3

Solution:

Given expression

20a3b4 + 25a2b2 + 10a5b3

Factor the each term

First term in the expression can be factored

20a3b4 = 2 . 2. 5 . a . a . a . b . b . b . b

Second term in the expression can be factored

25a2b2 = 5 . 5 . a . a . b . b

Last term in the expression can be factored

10a5b3 = 2 . 5 . a . a . a . a . a . b . b . b

Determine the greatest common factor for the expression 5a2b2

Using the distributive law the expression can be written as

20a3b4 + 25a2b2 + 10a5b3 = 5a2b2 (4ab2) + 5a2b2 (5) + 5a2b2 (2a3b)

                                          = 5a2b2 (4ab2 + 5 + 2a3b)

Answer:

20a3b4 + 25a2b2 + 10a5b3 = 5a2b2 (4ab2 + 2a3b + 5)