If $$250\sqrt2 x^3 - 5\sqrt5 y^3 = (5\sqrt2 x - \sqrt5 y) \times (Ax^2 + Bxy + Cy^2)$$, then the value of $$(A + C - \sqrt{10}B)$$ is:

$$250\sqrt2 x^3 - 5\sqrt5 y^3 = (5\sqrt2 x - \sqrt5 y) \times (Ax^2 + Bxy + Cy^2)$$    Eq.(i)

$$(a^3-b^3) = (a-b) (a^2+ab+b^2)$$

We know the above formula. By this, we can expand the equation which is given in the question to get the values of 'A', 'B' and 'C'.

$$(5\sqrt2 x)^3 - (\sqrt5 y)^3 = (5\sqrt2 x - \sqrt5 y) \times ((5\sqrt2x)^2 + 5\sqrt2x \times \sqrt5 y + (\sqrt5 y)^2)$$

$$250\sqrt2 x^3 - 5\sqrt5 y^3 = (5\sqrt2 x - \sqrt5 y) \times (50x^2 + 5\sqrt10 x y + 5y^2)$$

By comparing the Eq.(i) with the above equation, we can obtain the values of 'A', 'B' and 'C'.

A = 50, B = $$5\sqrt10$$, C = 5

Value of $$(A + C - \sqrt{10}B)$$ = $$(50 + 5 - \sqrt{10}\times5\sqrt10)$$

= (50 + 5 - 50)

= 5