Factorize the following expression : \( 2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 – 3\sqrt{6}abc \)
\[
2\sqrt{2}a^3 + 3\sqrt{3}b^3 + c^3 – 3\sqrt{6}abc
\]
\[
= (\sqrt{2}a)^3 + (\sqrt{3}b)^3 + c^3
– 3(\sqrt{2}a)(\sqrt{3}b)(c)
\]
\[
= (\sqrt{2}a + \sqrt{3}b + c)
\]
\[
\times
\left[
2a^2 + 3b^2 + c^2
– \sqrt{6}ab – \sqrt{2}ac – \sqrt{3}bc
\right]
\]