EXAMPLES:
Question:
Factor out the greatest common factor:
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$\,6x  8xy\,$
Answer:
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$2x(3  4y)$
Here's what's going on:
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$6x  8xy$ 
Ignore the plus/minus signs of the terms for the moment,
and find the greatest common factor of $\,6x\,$ and $\,8xy\,$, which is $\,2x\,$. 
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$= \overset{\text{gcf}}{\overbrace{(2x)}}(3) 
\overset{\text{gcf}}{\overbrace{(2x)}}(4y)$

Rename each term as the greatest common factor, times the remaining factors.
Eventually, you won't need to write down this intermediate step. 
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$= (2x)(3  4y)$ 
Use the distributive law, backwards! 
Question:
Factor out the greatest common factor:
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$\,3x^2y + 5x^2y^2\,$
Answer:
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$x^2y(3 + 5y)$
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.