Factor 5v^3-1080

$5 v^{3} - 1080$

Step 1

Factor $5$ out of $5 v^{3} - 1080$ .

Factor $5$ out of $5 v^{3}$ .

$5 (v^{3}) - 1080$

Factor $5$ out of $- 1080$ .

$5 v^{3} + 5 \cdot - 216$

Factor $5$ out of $5 v^{3} + 5 \cdot - 216$ .

$5 (v^{3} - 216)$

Step 2

Rewrite $216$ as $6^{3}$ .

$5 (v^{3} - 6^{3})$

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 $a = v$ and $b = 6$ .

$5 ((v - 6) (v^{2} + v \cdot 6 + 6^{2}))$

Step 4

Factor.

Simplify.

Move $6$ to the left of $v$ .

$5 ((v - 6) (v^{2} + 6 v + 6^{2}))$

Raise $6$ to the power of $2$ .

$5 ((v - 6) (v^{2} + 6 v + 36))$

Remove unnecessary parentheses.

$5 (v - 6) (v^{2} + 6 v + 36)$

Factor 5v^3-1080

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