Factor -9+121m^8n^8

$- 9 + 121 m^{8} n^{8}$

Factor $- 1$ out of $- 9 + 121 m^{8} n^{8}$ .

Reorder $- 9$ and $121 m^{8} n^{8}$ .

$121 m^{8} n^{8} - 9$

Factor $- 1$ out of $121 m^{8} n^{8}$ .

$- (- 121 m^{8} n^{8}) - 9$

Rewrite $- 9$ as $- 1 (9)$ .

$- (- 121 m^{8} n^{8}) - 1 (9)$

Factor $- 1$ out of $- (- 121 m^{8} n^{8}) - 1 (9)$ .

$- (- 121 m^{8} n^{8} + 9)$

Rewrite $9$ as $3^{2}$ .

$- (- 121 m^{8} n^{8} + 3^{2})$

Rewrite $121 m^{8} n^{8}$ as ${(11 m^{4} n^{4})}^{2}$ .

$- (- {(11 m^{4} n^{4})}^{2} + 3^{2})$

Reorder $- {(11 m^{4} n^{4})}^{2}$ and $3^{2}$ .

$- (3^{2} - {(11 m^{4} n^{4})}^{2})$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3$ and $b = 11 m^{4} n^{4}$ .

$- ((3 + 11 m^{4} n^{4}) (3 - (11 m^{4} n^{4})))$

Factor.

Simplify.

Multiply $11$ by $- 1$ .

$- ((3 + 11 m^{4} n^{4}) (3 - 11 (m^{4} n^{4})))$

Remove parentheses.

$- ((3 + 11 m^{4} n^{4}) (3 - 11 m^{4} n^{4}))$

Remove unnecessary parentheses.

$- (3 + 11 m^{4} n^{4}) (3 - 11 m^{4} n^{4})$

Factor -9+121m^8n^8

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