Question
If 512x3 - y3 = (8x - Ay) X
(Bx2 + y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.Solution
512x3 - y3 = (8x - Ay) X (Bx2 + y2 + Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 512x3 - y3 = (8x)3 - (1y)3 = (8x - y) X (64x2 + y2 + 8x X y) = (8x - y) X (64x2 + y2 + 8xy) So, (8x - Ay) X (Bx2 + y2 + Cxy)= (8x - y) X (64x2 + y2 + 8xy) On comparing coefficients of LHS and RHS, we get, A = 1, B = 64, and C = 8 So, 3 X (2A + 6B) - 2C = 3 X {2 X 1 + 6 X 64} - 2 X 8 = 3 X (2 + 384) - 16 = 3 X 386 - 16 = 1158 - 16 = 1142
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