I don't really understand how to calculate factorial moment for distributions besides just looking at the given formulas in my textbook. So say I want to calculate the E[X(X-1)] factorial moment for Poisson and Binomial distribution:

For Binomial distribution, we can see that E[X(X-1)]=$E[(X)\_{2}]$=E[x!/(x-2)!}= sum of p(x) x!/(x-2)!. Okay, what should I do next? 

I'm not entirely sure if there is any other changes for Poisson distribution... but seeing that the end result is a $\lambda$ makes me wonder what happens in between...