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

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

No vote yet

2 votes

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestThe 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 · 3 years, 4 months ago

Log in to reply

– Apoorv Singhal · 1 year, 5 months ago

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

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 · 1 year, 5 months ago

Log in to reply

– Mark Hennings · 1 year, 5 months ago

Provided that \(\{a,b,c\} = \{x,y,z\}\) ... correct. You could take out the factor of \(5\) as well.Log in to reply