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How to Factor Out Variables

You can factor out variables from the terms in an expression. You factor out variables the same way as you do numbers except that when you factor out powers of a variable, the smallest power that appears in any one term is the most that can be factored out.

Variables represent values; variables with exponents represent the powers of those same values.

In an expression such as

image0.png

the smallest power of a that appears in any term is

image1.png

is the greatest common factor. You can’t factor anything else out of each term:

image2.png

Check your work quickly by doing either of the following:

  • Multiply through (distribute) your answer in your head to be sure that the factored form is equivalent to the original form.

    This is the problem you began with, so you factored the variables out correctly!

  • Scan the terms in parentheses to make sure that they don’t share the same variable.

    The terms in parentheses don't share any common variables, so you're done!

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