Proving bounds for a function
By definition it's enough to show existence of $c&gt;0$, and, also existence of $N \in \mathbb{N}$, for which $f(n) \geqslant c g(n)$, when $n \gt N$. Of course, if it's possible to find $c$, then proof is also done.
In case of $(n + a)^b = \Omega(n^b)$, assuming $a,b&gt;0$, then choice $c=N=1$ fulfills definition, as we have $(n + a)^b \geqslant  n^b$.
BTW, holds also $(n + a)^b = O(n^b)$, so $(n + a)^b = \Theta(n^b)$.