Question
If 8x3Â - 125y3Â = (2x - Ay) X
(Bx2Â + 25y2Â + Cxy), then find the value of 3 X (2A + 6B) - 2C.Solution
8x3Â - 125y3Â = (2x - Ay) X (Bx2Â + 25y2Â - Cxy) We know that, a3Â - b3Â = (a - b) X (a2Â + b2Â + ab) So, 8x3Â - 125y3Â = (2x)Â 3Â - (5y)Â 3 = (2x - 5y) X (4x2Â + 25y2Â + 2x X 5y) = (2x - 5y) X (4x2Â + 25y2Â + 10xy) So,(2x - Ay) X (Bx2Â + 25y2Â + Cxy) = (2x - 5y) X (4x2Â + 25y2Â + 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
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