Precalculus Examples

$3 t^{3} - 81$

Step 1

Factor $3$ out of $3 t^{3} - 81$ .

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Step 1.1

Factor $3$ out of $3 t^{3}$ .

$3 (t^{3}) - 81$

Step 1.2

Factor $3$ out of $- 81$ .

$3 t^{3} + 3 \cdot - 27$

Step 1.3

Factor $3$ out of $3 t^{3} + 3 \cdot - 27$ .

$3 (t^{3} - 27)$

Step 2

Rewrite $27$ as $3^{3}$ .

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

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 $b = 3$ .

$3 ((t - 3) (t^{2} + t \cdot 3 + 3^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Move $3$ to the left of $t$ .

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

Step 4.1.2

Raise $3$ to the power of $2$ .

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

Step 4.2

Remove unnecessary parentheses.

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