The binomial series expansion for an expression of the form \((a+bx)^n\) where \(n\) is a Natural number is given by:

\((a+bx)^n=\tbinom{n}{0}(a)^n(bx)^{0}+\tbinom{n}{1}(a)^{n-1}(bx)^{1}+\tbinom{n}{2}(a)^{n-2}(bx)^{2}+...\tbinom{n}{k}(a)^{n-k}(bx)^{k}+...\tbinom{n}{n}(a)^{0}(bx)^{n}\)

In this example  \(n=\var{n}\),  \(a=\var{a}\)  and  \(b=\var{b}\).

So the first three terms of the binomial series expansion are:

 \(\var{a}^{\var{n}}+\tbinom{\var{n}}{\var{1}}\times\var{a}^{\var{n}-1}\times\var{b}^{1}+\tbinom{\var{n}}{2}\times\var{a}^{\var{n}-2}\var{b}^{2}\)

\(=\simplify{{a}^{n}}+\simplify{{n}*{a}^({n}-1)*{b}}x+\simplify{{n}*{n-1}*{a}^{{n}-2}*{b}^2/2x^2}\)