Factor, \(ab^3 - a^3 b + bc^3 - b^3 c + ca^3 - c^3 a\)

I've tried factoring it normally like taking out ab,bc,ca and then using difference of squares. Or taking a out of the first and last, b etc. And then using difference of cubes. But I can't seem to factor it any further.

I believe I'm supposed to use the Multivariable Factor Theorem but I can't figure out how to apply it, or how to use it in this case.

Any help would much appreciated!

Guest Jun 4, 2022