1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    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

    User Avatar
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?