Thread: moment generating function of a binomial random variable

Hey guys, I am trying to wrap my head around this problem. I understand everything except how they get to a certain point. Here is the problem:

Derive the moment generating function of a binomial random variable and then use your result to verify the formulas for the mean and variance given in the text.

the books solution:




The red arrow in the picture is where I am lost. I can not figure out how they got from the left side of the arrow to the right. Can someone help me out?

Thanks

Use the binomial theorem with and .

You should be able to figure it out from there.