Factor -81+a^4

$- 81 + a^{4}$

Step 1

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

$- 81 + {(a^{2})}^{2}$

Step 2

Rewrite $81$ as $9^{2}$ .

$- 9^{2} + {(a^{2})}^{2}$

Step 3

Reorder $- 9^{2}$ and ${(a^{2})}^{2}$ .

${(a^{2})}^{2} - 9^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a^{2}$ and $b = 9$ .

$(a^{2} + 9) (a^{2} - 9)$

Step 5

Simplify.

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

$(a^{2} + 9) (a^{2} - 3^{2})$

Factor.

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

$(a^{2} + 9) ((a + 3) (a - 3))$

Remove unnecessary parentheses.

$(a^{2} + 9) (a + 3) (a - 3)$

Factor -81+a^4

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