Here's the direct approach - it's just some common series index manipulations:
I'll write for "n choose a".
(now substitute r = i+1 in the 2nd sum)
(now peel off the r=10)
(note: C(9, 9) = 1)
(now peel off the i=0, set r = i)
(note signs in 2nd sum)
(note: C(9,0) = 1)
(now combine the sums)
Note that evaluating at .
Thus (treat the leading 1 as r=0).
Note that your book was wrong to exclude the , since is a 10th degree polynomial, but the answer your book gave was only a 9th degree polynomial.