Factorisation Problem

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

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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...

Mark Hennings - 7 years, 9 months ago

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

Apoorv Singhal - 5 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,

Apoorv Singhal - 5 years, 10 months ago

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

Mark Hennings - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$