Question Detail
Question
Find the coefficient of x⁶y⁶ in the binomial expansion of (2x² - y²)⁶
Correct Answer
Option D is the correct answer.
Detailed Explanation
In (2x² - y²)⁶, the general term is C(6,r) (2x²)^(6-r) (-y²)^r = C(6,r) 2^(6-r) x^(12-2r) (-1)^r y^(2r). For x⁶y⁶, we need 12-2r = 6 → 2r = 6 → r = 3, and 2r = 6 → r = 3, consistent. Then term = C(6,3) 2³ (-1)³ x⁶ y⁶ = 20 × 8 × (-1) × x⁶y⁶ = -160 x⁶y⁶.
Hint
Use binomial expansion and match powers of x and y.