Discrete Math Proof: $A\cup B$

The problem I'm having trouble proving is the following:

$A\cup B=(A\cap BC)\cup (AC\cap B)\cup (A\cap B)$, where C denotes complement of a set

The problem I'm having trouble proving is the following:

$A\cup B=(A\cap BC)\cup (AC\cap B)\cup (A\cap B)$, where C denotes complement of a set