Could someone give me guidelines on doing this question?
The coefficient of $\displaystyle x^r$ is:
$\displaystyle \displaystyle {9 \choose r} (-1)^r + {9 \choose r - 1} (-1)^{r-1}$.
Your job is to simplify this and hence get the answer.
Note:
$\displaystyle \displaystyle \frac{9!}{r! (9 - r)!} = \frac{9! (10 - r)}{r! (10 - r)!} $
$\displaystyle \displaystyle \frac{9!}{(r-1)! (10 - r)!} = \frac{9! r}{r! (10 - r)!} $
I've shown that there can be an expression involving x to the power r in a sigma expression. A term containg x to the power r and not any other power of x can not be found for the rth element. The books question doesn't make sense. The book has many errors in the answers section for this group.