﻿ Factoring out the Greatest Common Factor
FACTORING OUT THE GREATEST COMMON FACTOR

EXAMPLES:
Question: Factor out the greatest common factor: $\,6x - 8xy\,$
Answer: $2x(3 - 4y)$

Here's what's going on:
 $6x - 8xy$ Ignore the plus/minus signs of the terms for the moment, and find the greatest common factor of $\,6x\,$ and $\,8xy\,$, which is $\,2x\,$. $= \overset{\text{gcf}}{\overbrace{(2x)}}(3) - \overset{\text{gcf}}{\overbrace{(2x)}}(4y)$ Rename each term as the greatest common factor, times the remaining factors. Eventually, you won't need to write down this intermediate step. $= (2x)(3 - 4y)$ Use the distributive law, backwards!
Question: Factor out the greatest common factor: $\,3x^2y + 5x^2y^2\,$
Answer: $x^2y(3 + 5y)$

Note:   In the web exercise below, you would input this answer as:   x^2y(3 + 5y)
Notice that exponents are input using the ‘ ^ ’ key.
Variables must appear in the same order as in the original expression, going from left to right.
For example, although   yx^2(3 + 5y)   or   x^2y(5y + 3)   are correct answers, they are not recognized as correct.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
The Addition Property of Equality

Factor out the greatest common factor: