SOLUTION: Fully factor the following: 4a^2-(3a+1)^2 I believe that I need to use decomposition to answer this, but I can't understand how to approach it.

Algebra ->  Equations -> SOLUTION: Fully factor the following: 4a^2-(3a+1)^2 I believe that I need to use decomposition to answer this, but I can't understand how to approach it.      Log On


   

Question 106574: Fully factor the following:
4a^2-(3a+1)^2

I believe that I need to use decomposition to answer this, but I can't understand how to approach it.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Fully factor:
4a%5E2-%283a%2B1%29%5E2 Do you recognise this as the difference of two squares?
The difference of two squares is factorable as follows:
A%5E2-B%5E2+=+%28A-B%29%28A%2BB%29 In your problem, A = 2a while B = (3a+1), so...
4a%5E2-%283a%2B1%29%5E2+=+%282a-%283a%2B1%29%29%282a%2B%283a%2B1%29%29 Now simplfy this to get:
%28-a-1%29%285a%2B1%29
You can check this solution by multiplying these two factors to see if you get back the original expression. Let's try it using FOIL.
%28-a-1%29%285a%2B1%29+=+-5a%5E2%2B6a%2B1 = 4a%5E2-%289a%5E2%2B6a%2B1%29+=+4a%5E2-%283a%2B1%29%5E2