Given that (2x + y)3 - (x + 2y)3 = (x - y)[A(x2 + y2)+Bxy], the value of (2A - B) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1
(2x + y)3 - (x + 2y)3 = (x - y) [A(x2 + y2) + Bxy]
⇒ (2x)3 + y3 + 3 × 2x × y(2x + y) - (x)3 - (2y)3 - 3 × x × 2y (x + 2y) = (x - y) [Ax2 + Ay2 + Bxy]
⇒ 8x3 + y3 + 12x2y + 6xy2 - x3 - 8y3 - 6x2y - 12xy2 = [Ax3 + Axy2+ Bx2y - Ax2y - Ay3 - Bxy2]
⇒ 7x3 - 7y3 + 6x2y - 6xy2 = Ax3 - Ay3 + (B - A)x2y + (A - B)xy2
By comparison on LHS and RHS
⇒ A = 7, (B - A) = 6, (A - B) = - 6
⇒ (B - 7) = 6
⇒ B = 13
Hence (2A - B) = (2 × 7 - 13)
= 1