Factor x^6-x^2

$x^{6} - x^{2}$

Step 1

Factor $x^{2}$ out of $x^{6} - x^{2}$ .

Factor $x^{2}$ out of $x^{6}$ .

$x^{2} x^{4} - x^{2}$

Factor $x^{2}$ out of $- x^{2}$ .

$x^{2} x^{4} + x^{2} \cdot - 1$

Factor $x^{2}$ out of $x^{2} x^{4} + x^{2} \cdot - 1$ .

$x^{2} (x^{4} - 1)$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Factor.

Simplify.

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

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

Factor.

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 $b = 1$ .

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor x^6-x^2

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