Without finding the cubes, factorise : `(x-2y)^(3)+(2y-3z)^(3)+(3z-x)^ – InterviewSolution

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1.	Without finding the cubes, factorise : `(x-2y)^(3)+(2y-3z)^(3)+(3z-x)^(3)`
Answer» Let x-2y=a, 2y-3z=b and 3z-x=c `therefore " " a+b+c=x-2y+2y-3z+3z-x=0` `implies " " a^(3)+b^(3)+c^(3)=3abc` Hence, `(x-2y)^(3)+(2y--3z)^(3)+(3z-x)^(3)=3(x-2y)(2y-3z)(3z-x)`

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