The binomial series expansion for an expression of the form (1+bx)n where n is a non-natural number, is given by:

(1+bx)n=1+n(bx)+n(n−1)2!(bx)2+n(n−1)(n−2)3!(bx)3.......

In this example the expression in the bracket doesn't have a 1, so we have to divide by that first, giving

an(1+bax)n=an(1+n(bax)+n(n−1)2!(bax)2+n(n−1)(n−2)3!(bax)3.......)

In this example  n=12, a=5  and  b=11.

So the first three terms are

512(1+bax)12=512(1+(12)(115x)+(12)(12−1)2(115x)2)

(5+11x)12=2.2360679775+24.596747752510x−1.3528211264x2