If 27x3 - 8y3 = (3x - Ay) X (Bx2 + 4y2 + Cxy), then find the value of 3 X (2A + 6

Solution

27x³ - 8y³ = (3x - Ay) X (Bx² + 4y² + Cxy) We know that, a³ - b³ = (a - b) X (a² + b² + ab) So, 27x³ - 8y³ = (3x)³ - (2y)³ = (3x - 2y) X (9x² + 4y² + 3x X 2y) = (3x - 2y) X (9x² + 4y² + 6xy) So, (3x - Ay) X (Bx² + 4y² + Cxy) = (3x - 2y) X (9x² + 4y² + 6xy) On comparing coefficients of LHS and RHS, we get, A = 2, B = 9, and C = 6 So, 3 X (2A + 6B) - 2C = 3 X {2 X 2 + 6 X 9} - 2 X 6 = 3 X (4 + 54) - 12 = 3 X 58 - 12 = 174 - 12 = 162