Factoring out the Greatest Common Factor

Not quite ready for this web exercise? Practice finding greatest common factors first: Finding the Greatest Common Factor of Variable Expressions

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 $\,2x\,.$
$\cssId{s18}{= \overset{\text{gcf}}{\overbrace{(2x)}}(3)} \cssId{s19}{- \overset{\text{gcf}}{\overbrace{(2x)}}(4y)}$	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.

Practice

The examples above give instructions on how to input your answers.