Precalculus Examples

$x^{3} - 2 x + x$

Step 1

Add $- 2 x$ and $x$ .

$x^{3} - x$

Step 2

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

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Step 2.1

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

$x \cdot x^{2} - x$

Step 2.2

Factor $x$ out of $- x$ .

$x \cdot x^{2} + x \cdot - 1$

Step 2.3

Factor $x$ out of $x \cdot x^{2} + x \cdot - 1$ .

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

Step 3

Rewrite $1$ as $1^{2}$ .

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

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$x ((x + 1) (x - 1))$

Step 4.2

Remove unnecessary parentheses.

$x (x + 1) (x - 1)$