Respuesta :
Answer:
Option D.
Step-by-step explanation:
The given expression is
[tex](x^2-x)^9[/tex]
Here, n=9, p=x^2 adn q=-x.
kth term in the binomial expansion of [tex](p+q)^n[/tex] is
[tex]T_{r}=^nC_{r-1}p^{n-r+1}q^{r-1}[/tex]
First term of the binomial expansion of [tex](x^2-x)^9[/tex] is
[tex]T_{1}=^9C_{1-1}(x^2)^{9-1+1}(-x)^{1-1}=x^{18}[/tex]
Second term of the binomial expansion of [tex](x^2-x)^9[/tex] is
[tex]T_{2}=^9C_{2-1}(x^2)^{9-2+1}(-x)^{2-1}=9(x^16)(-x)=-9x^{17}[/tex]
Third term of the binomial expansion of [tex](x^2-x)^9[/tex] is
[tex]T_{3}=^9C_{3-1}(x^2)^{9-3+1}(-x)^{3-1}=9(x^14)(x^2)=36x^{16}[/tex]
Last or 10th term of the binomial expansion of [tex](x^2-x)^9[/tex] is
[tex]T_{10}=^9C_{10-1}(x^2)^{9-10+1}(-x)^{10-1}=1(x^0)(-x^9)=-x^{9}[/tex]
Therefore, the correct option is D.
