Precalculus Examples

$1 - 125 \tan^{3} (s)$

Step 1

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

$1^{3} - 125 \tan^{3} (s)$

Step 2

Rewrite $125 \tan^{3} (s)$ as ${(5 \tan (s))}^{3}$ .

$1^{3} - {(5 \tan (s))}^{3}$

Step 3

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 $a = 1$ and $b = 5 \tan (s)$ .

$(1 - (5 \tan (s))) (1^{2} + 1 (5 \tan (s)) + {(5 \tan (s))}^{2})$

Step 4

Simplify.

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Step 4.1

Multiply $5$ by $- 1$ .

$(1 - 5 \tan (s)) (1^{2} + 1 (5 \tan (s)) + {(5 \tan (s))}^{2})$

Step 4.2

One to any power is one.

$(1 - 5 \tan (s)) (1 + 1 (5 \tan (s)) + {(5 \tan (s))}^{2})$

Step 4.3

Multiply $5 \tan (s)$ by $1$ .

$(1 - 5 \tan (s)) (1 + 5 \tan (s) + {(5 \tan (s))}^{2})$

Step 4.4

Apply the product rule to $5 \tan (s)$ .

$(1 - 5 \tan (s)) (1 + 5 \tan (s) + 5^{2} \tan^{2} (s))$

Step 4.5

Raise $5$ to the power of $2$ .

$(1 - 5 \tan (s)) (1 + 5 \tan (s) + 25 \tan^{2} (s))$