Question

find the value of (x-y)^3+(y-z)^3+(z-x)^3​

Answer 1

Hii

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3( - x^2y + y^2x - y^2z + z^2y + x^2z - z^2x)

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Answer 2

(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

= (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)