Question #2834

Factorize-

(x-y)[sup]3[/sup]+(y-z)[sup]3[/sup]+(z-x)[sup]3[/sup]+(x+y)[sup]3[/sup]

(x-y)[sup]3[/sup]+(y-z)[sup]3[/sup]+(z-x)[sup]3[/sup]+(x+y)[sup]3[/sup]

Expert's answer

(x-y)^{3} + (y-z)^{3} + (z-x)^{3 }+ (x+y)^{3} = x^{3} - y^{3} -3xy(x-y) + y^{3} - z^{3} -3 yz(y-z) +z^{3} - x^{3} - 3zx(z-x) + x^{3}+y^{3} + 3xy(x+y) =

= x^{3} + y^{3} + 6xy^{2} - 3y^{2}z + 3yz^{2} - 3z^{2}x + 3zx^{2}

= x

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