Factorize the following expression : \( (x – 2y)^3 + (2y – 3z)^3 + (3z – x)^3 \)
\[
(x – 2y)^3 + (2y – 3z)^3 + (3z – x)^3
\]
\[
\text{Let }
a = (x – 2y),\quad
b = (2y – 3z),\quad
c = (3z – x)
\]
\[
a + b + c = 0
\]
\[
\therefore a^3 + b^3 + c^3 = 3abc
\]
\[
= 3(x – 2y)(2y – 3z)(3z – x)
\]