Find the coefficient of x^8 in the expansion of (x^2-4)^6

Answer 1

(r + 1)st term of this expansion T_{r + 1} = C(6,r)(x²)^{6 - r}(- 4)^r = C(6,r)(- 4)^rx^{12 - 2r}; so 12 - 2r = 8, r = 2..

So coefficient of x⁸: C(6,2)(-4)² = 6!/(2!4!)(- 4)² = 15·16 = 240