SOLUTION: What is the third term of the binomial expansion of {{{(x+2)^4}}}

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Question 313232: What is the third term of the binomial expansion of %28x%2B2%29%5E4
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

The Rth term of the binomial expansion of %28A+%2B+B%29%5EN is

%28matrix%282%2C1%2CN%2CR-1%29%29A%5E%28N-R%2B1%29%2AB%5E%28R-1%29

where %28matrix%282%2C1%2CN%2CR-1%29%29 is the same as the combinations of
N things taken R-1 at a time, which is often written (N)C(R-1) and
often called "N choose R-1".

Therefore the third term of the expansion %28x%2B2%29%5E4 is
found by substituting A=x, B=2, N=4, and R=3

%28matrix%282%2C1%2CN%2CR-1%29%29A%5E%28N-R%2B1%29%2AB%5E%28R-1%29
%28matrix%282%2C1%2C4%2C3-1%29%29x%5E%284-3%2B1%29%2A2%5E%283-1%29
%28matrix%282%2C1%2C4%2C2%29%29x%5E2%2A2%5E2
%284%21%2F%282%21%284-2%29%21%29%29x%5E2%2A4
%284%21%2F%282%212%21%29%29x%5E2%2A4
%2824%2F%282%2A2%29%29x%5E2%2A4
%2824%2F4%29x%5E3%2A4
6x%5E2%2A4
24x%5E2

Edwin