If 8x3 - 125y3 = (2x - Ay) X

Solution

8x³ - 125y³ = (2x - Ay) X (Bx² + 25y² - Cxy) We know that, a³ - b³ = (a - b) X (a² + b² + ab) So, 8x³ - 125y³ = (2x) ³ - (5y) ³ = (2x - 5y) X (4x² + 25y² + 2x X 5y) = (2x - 5y) X (4x² + 25y² + 10xy) So,(2x - Ay) X (Bx² + 25y² + Cxy) = (2x - 5y) X (4x² + 25y² + 10xy) On comparing coefficients of LHS and RHS, we get, A = 5, B = 4, and C = 10 So, 3 X (2A + 6B) - 2C = 3 X {2 X 5 + 6 X 4} - 2 X 10 = 3 X (10 + 24) - 20 = 3 X 34 - 20 = 102 - 20 = 82