Answer
$126x^5$
Work Step by Step
Our aim is to find the fifth term for $(x-1)^{9}$.
General formula:$(p+q)^n=\displaystyle \binom{n}{k}p^{n-k}q^k$
and $\displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}; k=2$
Now, $(x-1)^{9}=\displaystyle \binom{9}{4}(x)^{9-4}(-1)^4$
This implies,
$=\dfrac{9!}{4!(9-4)!}(x)^{5}(-1)^4$
$=\dfrac{9 \times 8 \times 6 \times 5!}{4 \times 3 \times 2 \times 1(5!)}(x)^{5}$
Thus,
$=126x^5$
