Question
If 64x3 - 343y3 = (4x - Ay) X
(Bx2 + 49y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.Solution
64x3 - 343y3 = (4x - Ay) X (Bx2 + 49y2 + Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 64x3 - 343y3 = (4x)3 - (7y)3 = (4x - 7y) X (16x2 + 49y2 + 4x X 7y) = (4x - 7y) X (16x2 + 49y2 + 28xy) So, (4x - Ay) X (Bx2 + 49y2 + Cxy) = (4x - 7y) X (16x2 + 49y2 + 28xy) On comparing coefficients of LHS and RHS, we get, A = 7, B = 16, and C = 28 So, 3 X (2A + 6B) - 2C = 3 X {2 X 7 + 6 X 16} - 2 X 28 = 3 X (14 + 96) - 56 = 3 X 110 - 56 = 330 - 56 = 274
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