(x+2)^10(x-1)的展開式中x^9的系數(shù)

數(shù)學(xué)人氣：309 ℃時(shí)間：2020-06-02 13:10:05

優(yōu)質(zhì)解答

1.取 (x+2)^10的x^9項(xiàng),C(10,1)=10,再取(x-1)的常數(shù)項(xiàng)-1,相乘得-10
2.取 (x+2)^10的x^8項(xiàng),C(10,2)=45,再取(x-1)的x項(xiàng),相乘得45
1.2.相加得
x^9的系數(shù)=35選項(xiàng)里沒這個(gè)答案 - -A.-160B. 160C .-179D. 1791. 取 (x+2)^10的x^9項(xiàng)，C(10,1)*2=20，再取(x-1)的常數(shù)項(xiàng)-1，相乘得-202. 取 (x+2)^10的x^8項(xiàng)，C(10,2)*2^2=180，再取(x-1)的x項(xiàng)，相乘得1801.2.相加得x^9的系數(shù)=160