Factor by Grouping x^3-x

$x^{3} - x$

Step 1

Factor out the GCF of $x$ from $x^{3} - x$ .

Factor out the GCF of $x$ from each term in the polynomial.

Factor out the GCF of $x$ from the expression $x^{3}$ .

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

Factor out the GCF of $x$ from the expression $- x$ .

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

Since all the terms share a common factor of $x$ , it can be factored out of each term.

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

Step 2

Rewrite $1$ as $1^{2}$ .

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$x ((x + 1) (x - 1))$