In the expansion of (2x + y)3 - (2x - y)3, the coefficient of x2y is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 24.
(2x + y)3 - (2x - y)3 = (2x + y - 2x + y)[(2x + y)2 + (2x - y)2 + (2x + y)(2x - y)]
[a3 - b3 = (a - b)(a2 + b2 + ab)]
⇒ (2x + y)3 - (2x - y)3 = 2y × [4x2 + y2 + 4xy + 4x2 + y2 - 4xy + 4x2 - 2xy + 2xy - y2]
⇒ (2x + y)3 - (2x - y)3 = 2y × [12x2 + y2]
⇒ (2x + y)3 - (2x - y)3 = 24x2y + 2y3
Co-efficient of x2y = 24