Factorize the following expression : \( 2\sqrt{2}a^3 + 16\sqrt{2}b^3 + c^3 – 12abc \)
\[
2\sqrt{2}a^3 + 16\sqrt{2}b^3 + c^3 – 12abc
\]
\[
= (\sqrt{2}a)^3 + (2\sqrt{2}b)^3 + c^3
– 3(\sqrt{2}a)(2\sqrt{2}b)(c)
\]
\[
= (\sqrt{2}a + 2\sqrt{2}b + c)
\]
\[
\times
\left[
2a^2 + 8b^2 + c^2
– 4ab – \sqrt{2}ac – 2\sqrt{2}bc
\right]
\]