Hello everyone. I was wondering if there was a fast way to figure out the following: THe question is: What is the cofficient of u^16v^2 in the binomial expansion of (u^2 + v)^10? Well the answer is 45. I know what the binomail theorem is: and I can put (u^2 + v)^10 in that form a = u^2 b = v n = 10 (10 choose 0)*(u^2)^10 + (10 choose 1)*(u^2)^(9)*v + (10 choose 2)*(u^2)^(8)*v^2....... Okay so i found (10 choose 2) is where the coefficent of the binomial expansion of (u^2 + v)^10. But is this how your supppose to do it? Write it out like that? Or is there a faster way? I also got 45 by just taking (10 choose 2) = 45. So my question is, is there another way to compute this? It looks like the professor did somthing like: (u^16)*v^2 = (u^2)^8*v^2 I see they equal eachother but i'm not sure how this is connecting things together and how its figuring out the co-efficent. ANy help would be great!