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[tex]P = a(b^4-c^4)+b(a^4-c^4)+c(a^4-b^4)[/tex]

My work:

1. [tex]P = a( (b^2)^2 - (c^2)^2 )+b( (a^2)^2 - (c^2)^2 ) + c( (a^2)^2 - (b^2)^2 )[/tex]

2. [tex]P = a[ (b^2+c^2) (b+c) (b-c) ] + b[ (a^2+c^2) (a+c) (a-c) ] + c[ (a^2+b^2) (a+b) (a-b) ][/tex]

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Final Answer

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[tex]P = a[ (b^2+c^2) (b+c) (b-c) ] + b[ (a^2+c^2) (a+c) (a-c) ] + c[ (a^2+b^2) (a+b) (a-b) ][/tex]

Can someone please double check my work. As far as I can see, that is the simplest form to which it can be factored.

Thanks,

Mitch