SOLUTION: Give the coefficient of the third term in the expansion of each of the following. (x+2y)^5

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Question 379705: Give the coefficient of the third term in the expansion of each of the following.
(x+2y)^5
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Give the coefficient of the third term in the expansion of each of the following.
(x+2y)5
The kth term of %28A+%2B+B%29%5EN is %28matrix%282%2C1%2CN%2Ck-1%29%29A%5E%28N-k%2B1%29B%5E%28k-1%29

where %28matrix%282%2C1%2CP%2CQ%29%29%22%22=%22%22P%21%2F%28Q%21%28P-Q%29%21%29

So the coefficient is merely %28matrix%282%2C1%2CN%2Ck-1%29%29

Plugging in 5 for N and 3 for k

%28matrix%282%2C1%2C5%2C3-1%29%29
 
%28matrix%282%2C1%2C5%2C2%29%29

5%21%2F%282%21%285-2%29%21%29%22%22=%22%22%285%2A4%2A3%2A2%2A1%29%2F%28%282%2A1%29%283%2A2%2A1%29%29%22%22=%22%2210

Edwin