Factorize each of the following expressions: (x/2 + y + z/3)^3 + (x/3 - 2y/3 + y)^3 + (-5x/6 - y/3 - 4z/3)^3

Question

Factorize each of the following expressions:

\((\frac{\text{x}}{2}+\text{y}+\frac{\text{z}}{3})^{3}\) + \((\frac{\text{x}}{3}-\frac{2y}{3}+\text{y})^{3}\) + \((-\frac{5\text{x}}{6}-\frac{y}{3}-\frac{4z}{3})^{3}\) 

Answer 1

Given,

\(=(\frac{\text{x}}{2}+\text{y}+\frac{\text{z}}{3})^{3}\) + \((\frac{\text{x}}{3}-\frac{2y}{3}+\text{z})^{3}\) + \((-\frac{\text{5x}}{6}-\frac{\text{y}}{3}-\frac{\text{4z}}{3})^{3}\)