Algebra Examples

$5 x^{3} - 135$

Step 1

Factor $5$ out of $5 x^{3} - 135$ .

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Step 1.1

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

$5 (x^{3}) - 135$

Step 1.2

Factor $5$ out of $- 135$ .

$5 x^{3} + 5 \cdot - 27$

Step 1.3

Factor $5$ out of $5 x^{3} + 5 \cdot - 27$ .

$5 (x^{3} - 27)$

Step 2

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

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

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 $a = x$ and $b = 3$ .

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

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 $x$ .

$5 ((x - 3) (x^{2} + 3 x + 3^{2}))$

Step 4.1.2

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

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

Step 4.2

Remove unnecessary parentheses.

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