Algebra Examples

$x - x^{3}$

Step 1

Factor

$x$ out of

$x - x^{3}$ .

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Step 1.1

Raise

$x$ to the power of

$1$ .

$x^{1} - x^{3}$

Step 1.2

Factor

$x$ out of

$x^{1}$ .

$x \cdot 1 - x^{3}$

Step 1.3

Factor

$x$ out of

$- x^{3}$ .

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

Step 1.4

Factor

$x$ out of

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

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

Step 2

Rewrite

$1$ as

$1^{2}$ .

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

Step 3

Factor.

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Step 3.1

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = 1$ and

$b = x$ .

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

Step 3.2

Remove unnecessary parentheses.

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

$x - x^{3}$

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