If $(16\sqrt{2}x^3 + 81\sqrt{3}y^3) \div (2\sqrt{2}x + 3\sqrt{3}y) = Ax^2 + By^2 + Cxy$, then find the value of $2A - 3B - 2\sqrt{6} C$.

7

a³ + b³ = (a + b)(a² + b² - ab)

= (16√2x³ + 81√3y³) ÷ (2√2x + 3√3y) = Ax² + By² + Cxy

= Ax² + By² + Cxy = [(2√2x + 3√3y)(8x² + 27y² - 2√2x × 3√3y)]/(2√2x + 3√3y)

= Ax² + By²  + Cxy = (8x² + 27y² - 2√2x × 3√3y)

= Ax² + By²  + Cxy = (8x² + 27y² - 6√6xy)

A = 8, B = 27 and C = -6√6

The value of $2A - 3B - 2\sqrt{6} C$ = $2 × 8  - 3 × 27  - 2\sqrt{6}  × -6√6 $ = 7