Factoring

[NadroJV13]

Hello there. This is my first post, I hope the first and last, I would like to try and get better at doing math on my own. However, there is always one problem in a bunch that gives problems. I have a problem dealing with factoring:

Instructions:Factor the expression completely

The Problem

4(a+b)^2-4(a-b)^2

I have pulled 4 out because it is a GCF. Then I tried solving the problem using difference of squares but nothing seems to be working for me.

Any help would be deeply appreciated. Thank you!!

 

[Loren]

Factoring out the 4 is a good start. From there you have at least two options. One is to expand the binomials and simplify the result. I think you will find that many terms "drop out". Another option is to substitute x for a+b and y for a-b giving you 4x[sup:1h084usf]2[/sup:1h084usf] - 4y[sup:1h084usf]2[/sup:1h084usf]. Factor the difference of two squares. Then plug back in the a+b and a-b in place of the x and y respectively. Simplify your result. In either case you will end up with a monomial.

 

[Denis]

(a+b)^2 - (a-b)^2
= a^2 + 2ab + b^2 - (a^2 - 2ab + b^2)
= a^2 + 2ab + b^2 - a^2 + 2ab - b^2
= 4ab