Binomial theorem and series

Question

I want to confirm some points about binomial series.

1. The expression must be of the form$(1+x)^n$.

2. $x<1$

   The part where I am confused is that while finding derivatives through first principle , i've come through cases where binomial series is applied when expression is of the form $(a+x)^n$ and it isn't mentioned if $x$ < 1.

Answer 1

HINT: Note that $$(a+x)^n = a^n \left(1+\frac{x}{a}\right)^n.$$ If $|x|<|a|$ then the expansion of $(1+y)^n$ for $|y|<1$ can be applied.