The absorption property of a boolean expression states that $(a \land b) \lor (a \land \lnot b) = a$. I wanted to prove it myself but ran into a bit of a snafu. Here's my attempt ($a \land b \equiv c$):
$$(a \land b) \lor (a \land \lnot b) = c \lor (a \land \lnot b) = (c \lor a) \land (c \lor \lnot b)=(ab \lor a) \land (ab \lor \lnot b) = (aa \lor ab) \land (a \lnot b \lor b \lnot b) = (a \lor ab) \land (a \lnot b)=aa \lnot b \lor a \lnot b = a \lnot b \lor 0=a \lnot b$$
I'm not sure where I went wrong because my answer is very close to the actual answer.
How about $a=a\land 1=a\land (b\lor \lnot b) = (a\land b)\lor (a\land \lnot b)$ ?