Question

若x的立方+x的十次方=a0+a1(x+1)+……+a9(x+1)的九次方+a10(x+1)的十次方,求a2

Answer 1

x^3+x^10=[(x+1)-1]^3+[(x+1)-1]^10

a2(x+1)^2=C(3,2)(x+1)^2×(-1)^(3-2)+C(10,2)(x+1)^2×(-1)^(10-2)

a2=-C(3,2)+C(10,2)=-3+45=42