Factoring cubic equation

bizkut

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.

HallsofIvy

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]

bizkut

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]

Gib Z

Notice the symmetry in the variables. Then, without loss of generality, treat it as a polynomial in a, and collect coefficients.

Feldoh

Yeah, I'd have to agree with Gib Z