Precalculus Examples

$\tan^{3} (x) - 1$

Step 1

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

$\tan^{3} (x) - 1^{3}$

Step 2

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 $a = \tan (x)$ and $b = 1$ .

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply $\tan (x)$ by $1$ .

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

Step 3.2

One to any power is one.

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