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Homework Help: Factoring cubic equation

  1. Jan 2, 2008 #1
    Factorising cubic equation

    Anyone here know how to factor this equation?

    1. The problem statement, all variables and given/known data

    [tex]a^{3}c-a^{3}b+b^{3}a-b^{3}c+c^{3}b-c^{3}a[/tex]

    3. The attempt at a solution

    I tried factoring by grouping but ended up getting nowhere.

    If anyone can factor this equation, please tell me step by step how you got it.
     
    Last edited: Jan 2, 2008
  2. jcsd
  3. Jan 3, 2008 #2

    HallsofIvy

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    Science Advisor

    Cubics are bad enough but this has 3 variables. This is not a complete factorization but I think the most simplified form is
    [tex](a^3c- ac^3)+ (b^3a- a^3b)+ (c^3b- b^3c)= ac(a^2- c^2)+ ab(b^2- a^2)+ bc(c^2- b^2)[/tex]
    [tex]= ac(a- c)(a+ c)+ ab(b- a)(b+ a)+ bd(c- b)(c+ b)[/tex]
     
  4. Jan 4, 2008 #3
    thanks, that will be ok.

    but if you could figure how to get this form, please let me know.
    [tex](a+b+c)(b-c)(c-a)(a-b)[/tex]
     
  5. Jan 5, 2008 #4

    Gib Z

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    Homework Helper

    Notice the symmetry in the variables. Then, without loss of generality, treat it as a polynomial in a, and collect coefficients.
     
  6. Jan 5, 2008 #5
    Yeah, I'd have to agree with Gib Z
     
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