Question
If 125x3 - 216y3 = (5x - Ay) X (Bx2 + 36y2 + Cxy), then find the value of 3 X (2A + 6
- B - 2C.
Solution
125x3 - 216y3 = (5x - Ay) X (Bx2 + 36y2 - Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 125x3 - 216y3 = (5x)3 - (6y)3 = (5x - 6y) X (25x2 + 36y2 + 5x X 6y) = (5x - 6y) X (25x2 + 36y2 + 30xy) So, (5x - Ay) X (Bx2 + 36y2 + Cxy) = (5x - 6y) X (25x2 + 36y2 + 30xy) On comparing coefficients of LHS and RHS, we get, A = 6, B = 25, and C = 30 So, 3 X (2A + 6B) - 2C = 3 X {2 X 6 + 6 X 25} - 2 X 30 = 3 X (12 + 150) - 60 = 3 X 162 - 60 = 486 - 60 = 426
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