If 343x3 - 27y3 = (7x - Ay) X

Solution

343x³ - 27y³ = (7x - Ay) X (Bx² + y² + Cxy) We know that, a³ - b³ = (a - b) X (a² + b² + ab) So, 343x³ - 27y³ = (7x)³ - (3y)³ = (7x - 3y) X (49x² + 9y² + 7x X 3y) = (7x - 3y) X (49x² + 9y² + 21xy) So, (7x - Ay) X (Bx² + y² + Cxy) = (7x - 3y) X (49x² + 9y² + 21xy) On comparing coefficients of LHS and RHS, we get, A = 3, B = 49, and C = 21 So, 3 X (2A + 6B) - 2C = 3 X {2 X 3 + 6 X 49} - 2 X 21 = 3 X (6 + 294) - 42 = 3 X 300 - 42 = 900 - 42 = 858