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