Finite Math Examples

$2 t^{4} - 16 t$

Step 1

Factor $2 t$ out of $2 t^{4} - 16 t$ .

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Step 1.1

Factor $2 t$ out of $2 t^{4}$ .

$2 t (t^{3}) - 16 t$

Step 1.2

Factor $2 t$ out of $- 16 t$ .

$2 t (t^{3}) + 2 t (- 8)$

Step 1.3

Factor $2 t$ out of $2 t (t^{3}) + 2 t (- 8)$ .

$2 t (t^{3} - 8)$

Step 2

Rewrite $8$ as $2^{3}$ .

$2 t (t^{3} - 2^{3})$

Step 3

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

$2 t ((t - 2) (t^{2} + t \cdot 2 + 2^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Move $2$ to the left of $t$ .

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

Step 4.1.2

Raise $2$ to the power of $2$ .

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

Step 4.2

Remove unnecessary parentheses.

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