Answer
$210x^6$
Work Step by Step
Our aim is to find the fifth term for $(x-1)^{10}$.
General formula:$(p+q)^n=\displaystyle \binom{n}{k}p^{n-k}q^k$
and $\displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}$
Now, $(x-1)^{10}=\displaystyle \binom{10}{4}(x)^{10-4}(-1)^4$
This implies,
$=\dfrac{10!}{4!(10-4)!}(x)^{6}(-1)^4$
$=\dfrac{ 10 \times 9 \times 8 \times 7 \times 6!}{4 \times 3 \times 2 \times 1(6!)}(x)^{6}$
Thus,
$=210x^6$