20030827, 06:31  #1 
Sep 2002
60_{10} Posts 
Factoring Problem
I'm having trouble with this problem:
Factor: (4)(a^2)(c^2)  (a^2  b^2 + c^2)^2 Thanks 
20030827, 07:59  #2 
Nov 2002
2·37 Posts 
==>
(4)(a^2)(c^2)  (a^2  b^2 + c^2)^2 =  (a + b + c)·(a + b  c)·(a  b  c)·(a  b + c) hope i could help you andi314 
20030829, 06:10  #3 
Sep 2002
2^{2}×3×5 Posts 
I have checked and the answer is correct, and I have accidentally found a way to find the factors, but it was through major guessing. Could anyone show how to factor this out fully?

20030829, 06:34  #4  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
There are online factorers. The one I frequently use is "Factoris" at http://wims.unice.fr/wims/wims.cgi It can factor an integer, a rational number, a polynomial or a rational function.
When given: 4(a^2)*(c^2)(a^2b^2+c^2)^2 Factoris returned: Quote:
Factoris doesn't use "*" for multiplication in its output even though it wants you to use it in input. :) Of course, Factoris doesn't tell you how to factor an expression. But one might get clues from its answers. 

20030830, 17:56  #5  
Jun 2003
12073_{8} Posts 
Re: Factoring Problem
Quote:
(4)(a^2)(c^2)  (a^2  b^2 + c^2)^2 ==> X^2  Y^2, where X = 2ac and Y = (a^2  b^2 + c^2) ==> (X+Y)(XY) ==> (2ac + a^2  b^2 + c^2)(2ac  a^2 + b^2  c^2) ==> [(a+c)^2  b^2] [b^2  (ac)^2] ==>[(a+c+b)(a+cb)] [(b+ac)(ba+c)] 

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