How to show these two Boolean expressions are the same?

Question

How do I show using the laws of Boolean algebra that: $$ (a \wedge c) \, \vee \, (a \wedge b) \, \vee \, (b \wedge c) \equiv (\bar{a} \wedge b \wedge c) \, \vee \, (a \wedge \bar{b} \wedge c) \, \vee \, (a \wedge b \wedge \bar{c}) \, \vee \, (a \wedge b \wedge c) $$

Answer 1

$a\land b = (a\land b \land c) \lor (a\land b \land \lnot c)$

$a\land c = (a\land b \land c) \lor (a\land \lnot b \land c)$

$b\land c = (a\land b \land c) \lor (\lnot a\land b \land c)$

Therefore

$(a\land b)\lor (a\land c)\lor ( b\land c)= (a\land b \land c) \lor (a\land b \land \lnot c)\lor (a\land \lnot b \land c)\lor (\lnot a\land b \land c)$