SOLUTION: Hello, here is my problem: (U^6 + V^6 + 2U^3V^3) / (U^3 -V^3 + U^2V –UV^2) The answer is= (U^2-UV+V^2)^2 / (U-V) I have been working on it for about three hours, I just need the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, here is my problem: (U^6 + V^6 + 2U^3V^3) / (U^3 -V^3 + U^2V –UV^2) The answer is= (U^2-UV+V^2)^2 / (U-V) I have been working on it for about three hours, I just need the      Log On


   



Question 16575: Hello, here is my problem:
(U^6 + V^6 + 2U^3V^3) / (U^3 -V^3 + U^2V –UV^2)
The answer is= (U^2-UV+V^2)^2 / (U-V)
I have been working on it for about three hours, I just need the steps to help me figure it out. Please and Thanks!

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, here we go. I hope you're good at factoring binomials and trinomials.
%28U%5E6+%2B+2U%5E3V%5E3+%2B+V%5E6%29%2F%28U%5E3+%2B+U%5E2V+-+UV%5E2+-+V%5E3%29
LET'S DO THE NUMERATOR FIRST: FACTOR IT.
U%5E6+%2B+2U%5E3V%5E3+%2B+V%5E6+=+%28U%5E3+%2B+V%5E3%29%28U%5E3+%2B+V%5E3%29 NOW FACTOR THE FACTORS WHICH ARE BOTH THE SUM OF TWO CUBES.

NOW WE'LL DO THE DENOMINATOR. FACTOR BY GROUPING.
%28U%5E3+%2B+U%5E2V%29+-+%28UV%5E2+%2B+V%5E3%29+=+U%5E2%28U+%2B+V%29+-+V%5E2%28+U+%2B+V%29 FACTOR THE (U + V)
%28U+%2B+V%29%28U%5E2+-+V%5E2%29 NOW FACTOR THE (U^2 - V^2), IT'S THE DIFFERENCE OF TWO SQUARES.
%28U+%2B+V%29%28U+%2B+V%29%28U+-+V%29 OK, NOW WE CAN PUT IT ALL BACK TOGETHER.

NOW, CANCEL THE (U + V)'S LEAVING:
%28%28U%5E2+-+UV+%2B+V%5E2%29%28U%5E2+-+UV+%2B+V%5E2%29%29%2F%28U+-+V%29 = %28U%5E2+-+UV+%2B+V%5E2%29%5E2%2F%28U+-+V%29 WE'RE DONE!