Trigonometry Examples

$\tan^{3} (x) + 27$

Step 1

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

$\tan^{3} (x) + 3^{3}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = \tan (x)$ and $b = 3$ .

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

Step 3

Simplify.

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Step 3.1

Multiply $3$ by $- 1$ .

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

Step 3.2

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

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