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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!

 Jun 4, 2022
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Factor   ab^3 - a^3b + bc^3 - b^3c + ca^3 - c^3a

 

-(a - b) (a - c) (b - c) (a + b + c)

 Jun 4, 2022

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