Factor t^4-16

$t^{4} - 16$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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

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

Factor.

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

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

Remove unnecessary parentheses.

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

Factor t^4-16

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