Find the value of
(x-y)^3 + (y-z)^3 +(z-x)^3
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(x-y)^3 + (y-z)^3 + (z-x)^3
= (x-y+y-z)( (x-y)^2 - (x-y)(y-z) + (y-z)^2 ) + (z-x)^3 .......[ formula a^3+b^3 = (a+b)(a^2-ab+b^2) ]
= (z-x) [ (z-x)^2 - (x-y)^2 - (y-z)^2 + (x-y)(y-z) ]
= (z-x) [ -2zx - 2y^2 + 2xy + 2yz + (x-y)(y-z) ]
= (z-x) [ 2x(y-z) - 2y(y-z) + (x-y)(y-z) ]
= (z-x) [ 2(x-y)(y-z) + (x-y)(y-z) ]
= 3 (x-y)(y-z)(z-x)
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