$A\unlhd G$ , $B\unlhd G$ and $C\unlhd G$ then $A(B∩C)$ is a normal subgroup of $G$ If $A$ normal to $G$ , $B$ normal to $G$ and $C$ normal to $G$ then how can I show that$$A(B∩C)\unlhd G$$ 
how can i solve this problem? Thanks!

This is simply the lattice of normal subgroups. Show that if $A, B$ are normal subgroups of $G$, then so is $A \cap B$ is normal, and $ AB$ is normal
