Is this simplification correct, and if so, what law does it illustrate? Can I simplify $(F \land \neg M ) \lor (F \land A) \lor (F \land M \land G)$ to $F \land (\neg M \lor A \lor (M \land G) )$ ? And if so, what law does this illustrate?

$(\color{blue}{F} \land \
eg M ) \lor (\color{blue}{F} \land A) \lor (\color{blue}{F} \land M \land G)$

We can use the **distributive law** to get:

$\color{blue}{F} \land (\
eg M \lor A \lor (M \land G) )$ You can simplify by first using commutativity of disjunction to obtain $$F \land( A \lor\lnot M \lor(M\land G))$$ and then $$F\land (A \lor((\lnot M\lor M) \land (\lnot M \lor G))$$

Which can be simplified to

$$F\land (A \lor \lnot M \lor G))$$