Trying to figure out how to transform this predicate from disjunctive normal form to conjunctive normal form (repost of an earlier question):

$$( P \land Q ) \lor ( R \land S ) \lor ( P \land S )$$

Re-write rule: distribution of conjunction over disjunction:
$$( S \land ( P \lor R ) ) \lor ( P \land Q )$$

"Add" $S \lor$ to each:
$$( S \lor S \land ( P \lor R ) ) \land ( S \lor ( P \land Q ) )$$

$S \lor S \land$ "cancel out":
$$( P \lor R ) \land ( S \lor ( P \land Q ) )$$

Re-write rule: Distribution of disjunction over conjunction:
$$( P \lor R ) \land ( P \lor S ) \land ( Q \lor S )$$

The rewrite rules I'm unsure of I have put in quotes.

Is the above a valid progression?