I know that I have to use the binomial theorem. So, in following the formula of ${(1+x)}^{n} = {n \choose 0}+{n \choose 1}{x}+{n \choose 2}{x}^{2}...+{n \choose k}{x}^{k}+...+{n \choose n}{x}^{n}$, I came up with ${200 \choose 99}$, but I am certain that is not all the way correct, if at all.
Can anyone help me with this problem?
Binomial theorem states that \begin{equation} (a+b)^n = \sum_{k=0}^n \binom{n}{k} a^k b^{n-k}. \end{equation} Let $a=2x, b=-3y, n=200,$ and $k=101$.