SOLUTION: Fator the following biomial. 25x^2 - 81y^2. I'm not sure how to solve this. I'm just alittle confused on how to do it. Thank you for the help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Fator the following biomial. 25x^2 - 81y^2. I'm not sure how to solve this. I'm just alittle confused on how to do it. Thank you for the help.      Log On


   

Question 101336: Fator the following biomial.
25x^2 - 81y^2.

I'm not sure how to solve this. I'm just alittle confused on how to do it.
Thank you for the help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
25x%5E2-81y%5E2 Do you see that this binomial is the difference of two squares?
%285x%29%5E2-%289y%29%5E2
The difference of two squares can be factored thus:
A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29 Applying this to your problem, we get:
25x%5E2-81y%5E2+=+%285x%29%5E2-%289y%29%5E2 = %285x%2B9y%29%285x-9y%29
You can confirm this by using the FOIL method to multiply the resultant factors:
%285x%2B9y%29%285x-9y%29+=+25x%5E2cross%28-45xy%29%2Bcross%2845xy%29-81y%5E2 The two middle terms drop out to leave you with:
25x%5E2-81y%5E2