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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