Question 379705
Give the coefficient of the third term in the expansion of each of the following. 

(x+2y)<sup>5</sup>
<pre>
The kth term of {{{(A + B)^N}}} is {{{(matrix(2,1,N,k-1))A^(N-k+1)B^(k-1)}}}

where {{{(matrix(2,1,P,Q))}}}{{{""=""}}}{{{P!/(Q!(P-Q)!)}}}

So the coefficient is merely {{{(matrix(2,1,N,k-1))}}}

Plugging in 5 for N and 3 for k

{{{(matrix(2,1,5,3-1))}}}
 
{{{(matrix(2,1,5,2))}}}

{{{5!/(2!(5-2)!)}}}{{{""=""}}}{{{(5*4*3*2*1)/((2*1)(3*2*1))}}}{{{""=""}}}{{{10}}}

Edwin</pre>