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

1 Answer
Apr 27, 2017

Answer:

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!