If (2x + y)3 - (x - 2y)3 = (x + 3y) [Ax2 + By2 + Cxy], then what is the value of (A + 2B + C)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10
x3 - y3 = (x - y)(x2 + y2 + xy)
(2x + y)3 - (x - 2y)3 = (2x + y - x + 2y) [(2x + y)2 + (x - 2y)2 + (2x + y)(x - 2y)]
(x + 3y) [4x2 + y2 + 4xy + x2 + 4y2 - 4xy + 2x2 - 4xy + xy - 2y2]
(x + 3y) [7x2 + 3y2 - 3xy]
A = 7B = 3C = - 3
(A + 2B + C) = 7 + 6 - 3 = 10