Factorize the following expression : \( 3\sqrt{3}a^3 – b^3 – 5\sqrt{5}c^3 – 3\sqrt{15}abc \)
\[
3\sqrt{3}a^3 – b^3 – 5\sqrt{5}c^3 – 3\sqrt{15}abc
\]
\[
= (\sqrt{3}a)^3 + (-b)^3 + (-\sqrt{5}c)^3
– 3(\sqrt{3}a)(-b)(-\sqrt{5}c)
\]
\[
= (\sqrt{3}a – b – \sqrt{5}c)
\]
\[
\times
\left[
3a^2 + b^2 + 5c^2
+ \sqrt{3}ab – \sqrt{15}ac – \sqrt{5}bc
\right]
\]