If 512x3 - y3 = (8x - Ay) X

Solution

512x³ - y³ = (8x - Ay) X (Bx² + y² + Cxy) We know that, a³ - b³ = (a - b) X (a² + b² + ab) So, 512x³ - y³ = (8x)³ - (1y)³ = (8x - y) X (64x² + y² + 8x X y) = (8x - y) X (64x² + y² + 8xy) So, (8x - Ay) X (Bx² + y² + Cxy)= (8x - y) X (64x² + y² + 8xy) On comparing coefficients of LHS and RHS, we get, A = 1, B = 64, and C = 8 So, 3 X (2A + 6B) - 2C = 3 X {2 X 1 + 6 X 64} - 2 X 8 = 3 X (2 + 384) - 16 = 3 X 386 - 16 = 1158 - 16 = 1142