If $8(x+y)^3-27(x-y)^3=(5 y-x)\left(A x^2+B y^2+C x y\right)$, then what is the value of (A + B - C) ?

36

8(x + y)³ - 27(x - y)³ = (5y - x)(Ax² + By² + Cxy)

= 8[x³ + y³ + 3xy(x + y)] - 27[x³ - y³ - 3xy(x - y)] = 5Ax²y + 5By³ + 5Cxy² - Ax³ - Bxy² - Cx²y

= - 19x³ + 35y³ + 105x²y - 57xy² = - Ax³ + 5By³ + 5Ax²y - Cx²y + 5Cxy² - Bxy² 

By comparing the values of A, B & C in LHS & RHS

= - 19x³ = - Ax³ 

A = 19 

=  35y³ = 5By³

B = 7

= 105x²y = 5Ax²y - Cx²y

= 105x²y = x²y(5A - C)

= 105 = 5A - C 

= 105 = 5 × 19 - C   [A = 19] 

C = - 10 

 (A + B - C) = 19 + 7 - (- 10) = 26 + 10 = 36