Factor x^4-1

$x^{4} - 1$

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

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

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

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

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 $b = 1$ .

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

Simplify.

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

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

Factor.

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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 $b = 1$ .

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

Remove unnecessary parentheses.

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

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