Q. 155.0( 4 Votes )

Factorize (x – 2y)3 + (2y – 3z)3 + (3z – x)3 without finding the cubes explicitly.

Answer :

As the expression is of the form of sum of three cubes, for factorizing, we will use the identity


a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)


Taking the 3abc term to the right hand side, we have


a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 – ab – bc – ca) + 3abc


Here, a = (x – 2y), b = (2y – 3z) & c = (3z – x)


a3 + b3 + c3 = (x – 2y)3 + (2y – 3z)3 + (3z – x)3


Observe that a + b + c = (x – 2y) + (2y – 3z) + (3z – x) = 0


a3 + b3 + c3 = 0 + 3abc = 3abc


(x – 2y)3 + (2y – 3z)3 + (3z – x)3 = 3(x – 2y)(2y – 3z)(3z – x)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.