How to find the inverse metric in this case?

Caroll, while proving the Newtonian limit takes $g_{ab} = eta_{ab} + h_{ab}$.

He then just writes down the inverse metric to 1st order as $g^{ab} = eta^{ab} – h^{ab}$.

I don’t see how this calculation has been done. It looks like some kind of Binomial theorem has been used but I don’t see how.

Can anyone help me with the steps in between and what the inverse metric will look like to 2nd or 3rd order in $h$.