If $$[8(x + y)^3 - 27(x - y)^3] \div (5y - x) = Ax^2 + Bxy + Cy^2$$, then the value of (A + B + C) is:

From the given question,

$$[8(x + y)^3 - 27(x - y)^3] \div (5y - x) = Ax^2 + Bxy + Cy^2$$

$$\Rightarrow [8(x + y)^3 - 27(x - y)^3] \div (5y - x)$$

$$\Rightarrow \dfrac{(2x+2y-3x+3y)(4(x+y)^2+9(x-y)^2+6(x-y)(x+y))}{5y-x}$$

$$\Rightarrow \dfrac{(5y-x)(4x^2+4y^2+8xy+9x^2+9y^2-18xy+6x^2-6y^2)}{5y-x}$$

$$\Rightarrow \dfrac{(5y-x)(19x^2+7y^2-10xy)}{(5y-x)}$$

$$\Rightarrow 19x^2+7y^2-10xy=Ax^2 + Bxy + Cy^2$$

Comparing both side with the respective terms,

$$\Rightarrow A=19, B=-10, C=7$$

Hence, A+B+C$$=19-10+7=16$$