Simplify $((p\wedge q) \vee (\neg p \wedge r) \vee (q \wedge r))$

Question

$((p\wedge q) \vee (\neg p \wedge r) \vee (q \wedge r))$

$\iff$ $(p\wedge q) \vee r\wedge(\neg p\vee q)$ (Distributive Law)

Not really sure where to go from here, need some hints please.

Answer 1

It helps that $(q \wedge r) \implies ((p\wedge q) \vee (\neg p \wedge r)).$

Answer 2

Hint:

$$[(p \wedge q) \vee (\neg p \wedge r) \vee (q \wedge r)]$$

$$\equiv [(p \wedge q) \vee (q \wedge r) \vee (\neg p \wedge r)] $$ its happens because of the commutativity of $\vee$

Then apply the Distributive Law

$$\equiv [q \wedge(p \vee r) \vee (\neg p \wedge r) ]$$

and from here should be easy to simplify it.