Factor p^4-81

$p^{4} - 81$

Step 1

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

${(p^{2})}^{2} - 81$

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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

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

Factor.

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

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

Remove unnecessary parentheses.

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

Factor p^4-81

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