If 64x3 - 343y3 = (4x - Ay) X

Solution

64x³ - 343y³ = (4x - Ay) X (Bx² + 49y² + Cxy) We know that, a³ - b³ = (a - b) X (a² + b² + ab) So, 64x³ - 343y³ = (4x)³ - (7y)³ = (4x - 7y) X (16x² + 49y² + 4x X 7y) = (4x - 7y) X (16x² + 49y² + 28xy) So, (4x - Ay) X (Bx² + 49y² + Cxy) = (4x - 7y) X (16x² + 49y² + 28xy) On comparing coefficients of LHS and RHS, we get, A = 7, B = 16, and C = 28 So, 3 X (2A + 6B) - 2C = 3 X {2 X 7 + 6 X 16} - 2 X 28 = 3 X (14 + 96) - 56 = 3 X 110 - 56 = 330 - 56 = 274