Factor -27u^3+125

$- 27 u^{3} + 125$

Step 1

Factor $- 1$ out of $- 27 u^{3} + 125$ .

Factor $- 1$ out of $- 27 u^{3}$ .

$- (27 u^{3}) + 125$

Rewrite $125$ as $- 1 (- 125)$ .

$- (27 u^{3}) - 1 (- 125)$

Factor $- 1$ out of $- (27 u^{3}) - 1 (- 125)$ .

$- (27 u^{3} - 125)$

Step 2

Rewrite $27 u^{3}$ as ${(3 u)}^{3}$ .

$- ({(3 u)}^{3} - 125)$

Step 3

Rewrite $125$ as $5^{3}$ .

$- ({(3 u)}^{3} - 5^{3})$

Step 4

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 $a = 3 u$ and $b = 5$ .

$- ((3 u - 5) ({(3 u)}^{2} + 3 u \cdot 5 + 5^{2}))$

Step 5

Factor.

Simplify.

Apply the product rule to $3 u$ .

$- ((3 u - 5) (3^{2} u^{2} + 3 u \cdot 5 + 5^{2}))$

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

$- ((3 u - 5) (9 u^{2} + 3 u \cdot 5 + 5^{2}))$

Multiply $5$ by $3$ .

$- ((3 u - 5) (9 u^{2} + 15 u + 5^{2}))$

Raise $5$ to the power of $2$ .

$- ((3 u - 5) (9 u^{2} + 15 u + 25))$

Remove unnecessary parentheses.

$- (3 u - 5) (9 u^{2} + 15 u + 25)$

Factor -27u^3+125

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