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Re: Factoring problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg35503] Re: [mg35499] Factoring problem
*From*: BobHanlon at aol.com
*Date*: Wed, 17 Jul 2002 02:08:48 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 7/16/02 6:21:34 AM, shodgen at mindspring.com writes:
>I've decided to see if any of you can factor this eq. since it's not
>possible to have Mathematica show intermediate steps when factoring. This
>is a problem from my precalc book, and the instructor of the class hasn't
>been able to get to the final answer either. I've tried and tried using
>grouping in various ways, as well as other techniques.
>
>I'd appreciate it if anyone can figure this out, since I just can't get
>over
>this problem.
>
>Original problem:
> y^4 - (p + q)*y^3 + (p^2*q + p*q^2)*y - p^2*q^2
>Answer in book:
> (y^2 - p*q)*(y - p)*(y - q)
>
Since you know the answer, work the problem backwards.
(y^2 - p*q)*Expand[(y - p)*(y - q)]
((-p)*q + y^2)*(p*q - p*y - q*y + y^2)
% // Expand
(-p^2)*q^2 + p^2*q*y + p*q^2*y - p*y^3 - q*y^3 + y^4
%//Collect[#,y]&
(-p^2)*q^2 + (p^2*q + p*q^2)*y + (-p - q)*y^3 + y^4
Bob Hanlon
Chantilly, VA USA
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