find the coefficient of the term containing y^9 in the expansion of (-x+2y)^12

Answer 1

Term (k+1)-st T_k+1 = C(12,k)·(-x)^12-k(2y)^k. So, y^k = y⁹, k = 9 and we have 10-th term.

T₁₀ = C(12, 9)·(-x)³(2y)⁹ = - 220·2⁹x³y⁹ = - 112640x³y⁹

^{So, coefficient is - 112640}