Question

factorize: (x-y)^3+(y-z)^3+(z-x)^3​

Answer 1

Answer:

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Step-by-step explanation:

We know the corollary: if a+b+c=0 then a3+b3+c3=3abc

Using the above identity taking a=x−y, b=y−z and c=z−x, we have a+b+c=x−y+y−z+z−x=0 then the equation (x−y)3+(y−z)3+(z−x)3 can be factorised as follows:

(x−y)3+(y−z)3+(z−x)3=3(x−y)(y−z)(z−x)

Hence, (x−y)3+(y−z)3+(z−x)3=3(x−y)(y−z)(z−x)