Factor 5x^3-5

$5 x^{3} - 5$

Step 1

Factor $5$ out of $5 x^{3} - 5$ .

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

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

Factor $5$ out of $- 5$ .

$5 (x^{3}) + 5 (- 1)$

Factor $5$ out of $5 (x^{3}) + 5 (- 1)$ .

$5 (x^{3} - 1)$

Step 2

Rewrite $1$ as $1^{3}$ .

$5 (x^{3} - 1^{3})$

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 $a = x$ and $b = 1$ .

$5 ((x - 1) (x^{2} + x \cdot 1 + 1^{2}))$

Step 4

Factor.

Simplify.

Multiply $x$ by $1$ .

$5 ((x - 1) (x^{2} + x + 1^{2}))$

One to any power is one.

$5 ((x - 1) (x^{2} + x + 1))$

Remove unnecessary parentheses.

$5 (x - 1) (x^{2} + x + 1)$

Factor 5x^3-5

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