Question

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

Answer 1

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(5a^2 - 20)`

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.

`5a(a^2 - 4)`

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 `(a-2)(a+2)` when factored. Hence, your answer is:

`5a(a-2)(a+2)`

I hope that helps!