# Factorisation Problem

$$(y-z)^5 + (z-x)^5 + (x-y)^5$$. Factorize this. Please help me as soon as possible.

Note by Kumar Ashutosh
4 years, 9 months ago

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The polynomial equals $$0$$ if you put $$x=y$$, $$y=z$$ or $$x=z$$. Thus $$x-y$$, $$y-z$$ and $$z-x$$ are all factors. See where that takes you...

- 4 years, 9 months ago

It should be (x-y)(y-z)(z-x)[5(a^2+b^2+c^2)-5(ab+bc+ca)] .

- 2 years, 10 months ago

It should be (x-y)(y-z)(z-x)[5(a^2+b^2+c^2)-5(ab+bc+ca)] .I am quite sure about it.Tell me if I am wrong,

- 2 years, 10 months ago

Provided that $$\{a,b,c\} = \{x,y,z\}$$ ... correct. You could take out the factor of $$5$$ as well.

- 2 years, 10 months ago