# How do you simplify 1 - 125tan^3s?

Mar 16, 2018

$\left(1 - 125 {\tan}^{3} s\right) = \left(1 - 5 \tan s\right) \left(1 + 5 \tan s + 25 {\tan}^{2} s\right)$

#### Explanation:

To simplify $1 - 125 {\tan}^{3} s$

It is in the form ${a}^{3} - {b}^{3}$

We know ${a}^{3} - {b}^{3} = \left(a - b\right) \cdot \left({a}^{2} + a b + {b}^{2}\right)$

Hence $\left(1 - 125 {\tan}^{3} s\right) = \left(1 - 5 \tan s\right) \left(1 + 5 \tan s + 25 {\tan}^{2} s\right)$