Factor r^4-1

$r^{4} - 1$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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

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

Factor.

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

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

Remove unnecessary parentheses.

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

Factor r^4-1

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