Factorize : `2sqrt(2)a^3+8b^3-27 c^3+18sqrt(2)a b c`

Explanation

To factorize the expression \(2\sqrt{2}a^3 + 8b^3 - 27c^3 + 18\sqrt{2}abc\), we can follow these steps:

### Step 1: Rewrite the expression
We want to express the given polynomial in a form that resembles the sum of cubes. We can rewrite \(2\sqrt{2}a^3\) as \((\sqrt{2}a)^3\), \(8b^3\) as \((2b)^3\), and \(-27c^3\) as \(- (3c)^3\).

So, we rewrite the expression:
\[
2\sqrt{2}a^3 + 8b^3 - 27c^3 + 18\sqrt{2}abc = (\sqrt{2}a)^3 + (2b)^3 - (3c)^3 + 18\sqrt{2}abc
...