Factorize the following expression : \( (3x – 2y)^3 + (2y – 4z)^3 + (4z – 3x)^3 \)
\[
(3x – 2y)^3 + (2y – 4z)^3 + (4z – 3x)^3
\]
\[
\text{Let }
a = (3x – 2y),\quad
b = (2y – 4z),\quad
c = (4z – 3x)
\]
\[
a + b + c = 0
\]
\[
\therefore a^3 + b^3 + c^3 = 3abc
\]
\[
= 3(3x – 2y)(2y – 4z)(4z – 3x)
\]