Algebra Examples

$a^{3} - a$

Step 1

Factor

$a$ out of

$a^{3} - a$ .

Tap for more steps...

Step 1.1

Factor

$a$ out of

$a^{3}$ .

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

Step 1.2

Factor

$a$ out of

$- a$ .

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

Step 1.3

Factor

$a$ out of

$a \cdot a^{2} + a \cdot - 1$ .

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

Step 2

Rewrite

$1$ as

$1^{2}$ .

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

Step 3

Factor.

Tap for more steps...

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

$a = a$ and

$b = 1$ .

$a ((a + 1) (a - 1))$

Step 3.2

Remove unnecessary parentheses.

$a (a + 1) (a - 1)$