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Math Help - Factoring question

  1. #1
    Newbie
    Joined
    Mar 2010
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    Factoring question

    Hi, I am factoring somewhat complex polynomials. For example this one:
     <br />
a^3+b^3+c^3-3abc =<br />
     <br />
= a^3+b^3+c^3-3abc-3a^2b+3^2b-3ab^2+3ab^2<br />
= (a+b+b)(a^2+b^2+c^2-ab-ac-bc )<br />
    I only know to solve this kind of problems by guessing ( try to expand polynomial ). Is there a way to solve it by applying some algorithm?
    Also link to some material that explains this topic would be great.
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  2. #2
    Super Member
    Joined
    Jun 2009
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    Hi dontoo, welcome to MHF.
    a^3 + b^3 + c^3 -3abc = (a+b)^3 + c^3 -3abc-3ab^2 - 3a^2b
    = [(a+b+c)[(a+b)^2 + c^2 -(a+b)c] - 3ab(a+b+c)
    = (a+b+c)[a^2 + b^2 +2ab -ac - bc -3ab]
    = (a+b+c)(a^2+b^2+c^2-ab-bc-ac)
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  3. #3
    Newbie
    Joined
    Mar 2010
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    Thx for your replay. Is there is the way to solve it using polynomial zeros ( roots )?I don't want to guess how to expand polynomial.
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