# How do you factor completely -a^3-100a?

Jun 28, 2016

$- {a}^{3} - 100 a = - a \left({a}^{2} + 100\right) = - a \left(a - 10 i\right) \left(a + 10 i\right)$

#### Explanation:

$- {a}^{3} - 100 a$

= $- a \left({a}^{2} + 100\right)$

If we domain is real numbers, we cannot factorize it further.

However, if domain is complex numbers above is equal to

$- a \left[{a}^{2} - 10 a i + 10 a i - 100 {i}^{2}\right]$

= $- a \left[a \left(a - 10 i\right) + 10 i \left(a - 10 i\right)\right]$

= $- a \left(a - 10 i\right) \left(a + 10 i\right)$