what is the coefficient of the last term in the binomial expansion of (x + 1)^9?\n0\n1\n9\n10

Explanation:

Step1: Recall binomial theorem

The binomial expansion of $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$. For $(x + 1)^9$, $a=x$, $b = 1$, and $n=9$.

Step2: Find the last - term

The last term occurs when $k = 9$. Then the term is $\binom{9}{9}x^{9-9}\times1^{9}$.

Step3: Calculate the binomial coefficient

We know that $\binom{n}{k}=\frac{n!}{k!(n - k)!}$. When $n = 9$ and $k = 9$, $\binom{9}{9}=\frac{9!}{9!(9 - 9)!}=\frac{9!}{9!0!}=1$ (since $0!=1$).

Answer:

1