Question 313232
<pre><b>
The Rth term of the binomial expansion of {{{(A + B)^N}}} is

{{{(matrix(2,1,N,R-1))A^(N-R+1)*B^(R-1)}}}

where {{{(matrix(2,1,N,R-1))}}} 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 {{{(x+2)^4}}} is
found by substituting A=x, B=2, N=4, and R=3

{{{(matrix(2,1,N,R-1))A^(N-R+1)*B^(R-1)}}}
{{{(matrix(2,1,4,3-1))x^(4-3+1)*2^(3-1)}}}
{{{(matrix(2,1,4,2))x^2*2^2}}}
{{{(4!/(2!(4-2)!))x^2*4}}}
{{{(4!/(2!2!))x^2*4}}}
{{{(24/(2*2))x^2*4}}}
{{{(24/4)x^3*4}}}
{{{6x^2*4}}}
{{{24x^2}}}

Edwin</pre></b>