Factor a^4-16

$a^{4} - 16$

Step 1

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

${(a^{2})}^{2} - 16$

Step 2

Rewrite $16$ as $4^{2}$ .

${(a^{2})}^{2} - 4^{2}$

Step 3

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

$(a^{2} + 4) (a^{2} - 4)$

Step 4

Simplify.

Rewrite $4$ as $2^{2}$ .

$(a^{2} + 4) (a^{2} - 2^{2})$

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 $b = 2$ .

$(a^{2} + 4) ((a + 2) (a - 2))$

Remove unnecessary parentheses.

$(a^{2} + 4) (a + 2) (a - 2)$

Factor a^4-16

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