\[{x}^{3}-x\]

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Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

{x}^{3}

and

-x

It is

1

What is the highest degree of $x$ that divides evenly into

{x}^{3}

and

-x

It is

x

Multiplying the results above,

The GCF is

x

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GCF =

x

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

x(\frac{{x}^{3}}{x}-\frac{x}{x})

Simplify each term in parentheses.

x({x}^{2}-1)

Rewrite

{x}^{2}-1

in the form

{a}^{2}-{b}^{2}

, where

a=x

and

b=1

x({x}^{2}-{1}^{2})

Use Difference of Squares:

{a}^{2}-{b}^{2}=(a+b)(a-b)

x(x+1)(x-1)

Done

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