# How do you factor 5a^3-20a?

Apr 27, 2017

See below.

#### Explanation:

In order to factor, you are looking for similarities between terms. So, what is similar you ask? The first thing I would notice is that both terms contain $a$. Therefore, the first step I would take is to factor out a.

$a \left(5 {a}^{2} - 20\right)$

Are there more similarities, you might ask? Well, I would say yes. Both terms contain either 5 or a multiple of 5. So the second step I would take is to factor out the 5.

$5 a \left({a}^{2} - 4\right)$

So, can more stuff be done? Well, I would say yes once more. Actually, ${a}^{2} - 4$ is a characteristic pattern that you will recognize to be $\left(a - 2\right) \left(a + 2\right)$ when factored. Hence, your answer is:

$5 a \left(a - 2\right) \left(a + 2\right)$

I hope that helps!