ok, 1 bionimial theorem coming right up
for a binomial expansion of (a+b)^n
the kth term is
[tex] \left(\begin{array}{ccc}n\\k-1\end{array}\right)a^{n-(r-1)}b^{k-1}[/tex]
[tex] \left(\begin{array}{ccc}n\\k-1\end{array}\right) [/tex] means [tex] \frac{n!}{(k-1)!(n-(k-1))!} [/tex]
n is 5
4th term
4-1=3
and a=2x
b=5
so
[tex] \left(\begin{array}{ccc}5\\4-1\end{array}\right)(2x)^{5-(4-1)}5^{4-1}[/tex]
[tex] \left(\begin{array}{ccc}5\\3\end{array}\right)(2x)^{2}5^{3}[/tex]
[tex] \left(\begin{array}{ccc}5\\3\end{array}\right)(2x)^{2}5^{3}[/tex]
(10)(4x^2)(125)
5000x^2 is the 4th term
