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

Note by Kumar Ashutosh 4 years, 1 month 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...

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

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,

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

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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...

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

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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,

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

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