Factoring Problem
I'm having trouble with this problem:
Factor: (4)(a^2)(c^2)  (a^2  b^2 + c^2)^2 Thanks 
==>
(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 
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?

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]Warning. You have entered an ambiguous formula, whose interpretation by wims may differ from what you meant. Please check the formula. Please always use ``*'' for multiplication, and always enclose function arguments in parentheses. (For experts. If you don't want wims to interprete your expression, start it with the string ``11+''.) Factorization of the polynomial 4*(a^2)*(c^2)(a^2b^2+c^2)^2 into irreducible components over Z : a4 + (2c2 + 2b2) a2 + (c4 + 2b2 c2  b4)= (cba)(cb+a)(c+ba)(c+b+a) Remark. Factorization of multivariate polynomials is only implemented over Z for the time being.[/quote] In the nexttolast line, Factoris superscripts the exponents, but that formatting is lost in my cutandpasting the text here. That is, what is meant is a^4 + (2c^2 + 2b^2) a^2 + (c^4 + 2b^2 c^2  b^4) = (cba)(cb+a)(c+ba)(c+b+a) 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 [u]how[/u] to factor an expression. But one might get clues from its answers. 
Re: Factoring Problem
[quote="asdf"]I'm having trouble with this problem:
Factor: (4)(a^2)(c^2)  (a^2  b^2 + c^2)^2 Thanks[/quote] Soln: (I am omitting the * for multiplication) (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)] 
All times are UTC. The time now is 16:58. 
Powered by vBulletin® Version 3.8.11
Copyright ©2000  2022, Jelsoft Enterprises Ltd.