Question
If 343x3 - 27y3 = (7x - Ay) X
(Bx2 + y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.Solution
343x3 - 27y3 = (7x - Ay) X (Bx2 + y2 + Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 343x3 - 27y3 = (7x)3 - (3y)3 = (7x - 3y) X (49x2 + 9y2 + 7x X 3y) = (7x - 3y) X (49x2 + 9y2 + 21xy) So, (7x - Ay) X (Bx2 + y2 + Cxy) = (7x - 3y) X (49x2 + 9y2 + 21xy) On comparing coefficients of LHS and RHS, we get, A = 3, B = 49, and C = 21 So, 3 X (2A + 6B) - 2C = 3 X {2 X 3 + 6 X 49} - 2 X 21 = 3 X (6 + 294) - 42 = 3 X 300 - 42 = 900 - 42 = 858
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