In https://www.youtube.com/watch?v=0as464WmfCo it is mentioned that the following is simplified via the "absorption" law: $$A + \widehat{A}B = A + B.$$
However https://www.youtube.com/watch?v=tWU1mGCT_34 at around 4:40 it states this is not an example of the absorption law.
So by what rule is the above simplified (assuming the first video had it correct)?
It is not the absorption law, it is the distributive law, followed by complementation:
$$\begin{align} A + \overline{A}B & = (A+\overline{A})(A+B) \\ & = 1(A+B)\\ & = A+B \end{align}$$