Writing a Given Term of a Binomial Expansion

Find the tenth term of ${(x + 2 y)}^{16}$ without fully expanding the binomial.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Because we are looking for the tenth term, $r + 1 = 10,$ we will use $r = 9$ in our calculations.
$(\begin{matrix} n \\ r \end{matrix}) x^{n - r} y^{r}$

$(\begin{matrix} 16 \\ 9 \end{matrix}) x^{16 - 9} {(2 y)}^{9} = 5, 857, 280 x^{7} y^{9}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the sixth term of ${(3 x - y)}^{9}$ without fully expanding the binomial.

How did it go?