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