Factor r^4-1296

$r^{4} - 1296$

Step 1

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

${(r^{2})}^{2} - 1296$

Step 2

Rewrite $1296$ as $36^{2}$ .

${(r^{2})}^{2} - 36^{2}$

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 $b = 36$ .

$(r^{2} + 36) (r^{2} - 36)$

Step 4

Simplify.

Rewrite $36$ as $6^{2}$ .

$(r^{2} + 36) (r^{2} - 6^{2})$

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 $b = 6$ .

$(r^{2} + 36) ((r + 6) (r - 6))$

Remove unnecessary parentheses.

$(r^{2} + 36) (r + 6) (r - 6)$

Factor r^4-1296

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