If (2x + 3y)3 - (2x - 3y)3 = 3y[Ax2 + By2], then what is the value of (A - B)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 6.
(2x + 3y)3 − (2x − 3y)3 = 3y[Ax2 + By2]
a3 − b3 = (a − b)(a2 + ab + b2)
(2x + 3y)3 − (2x − 3y)3 = [(2x + 3y) − (2x − 3y)] × [(2x + 3y)2 + (2x + 3y)(2x − 3y) + (2x − 3y)2]
[(2x + 3y)2 + (2x + 3y)(2x − 3y) + (2x − 3y)2] = [4x2 + 12xy + 9y2] + [4x2 − 9y2] + [4x2 − 12xy + 9y2]
⇒ 6y(12x2 + 9y2) = 3y(24x2 + 18y2)
3y[Ax2 + By2] = 3y(24x2 + 18y2)
⇒ A − B = 24 − 18 = 6