discrete mathematics – Find if the statement is true or false, and prove directly.

For all sets, A ∩ (B ⋃ C) = (A ∩ B) ⋃ (A ∩ C).

I am supposed to prove if this is true or not. I have tried X ∈ P(A ∩ B) iff X ⊆ A ∩ B iff X ⊆ A and X ⊆ B, but don’t know how else to progress. Forgive me if I am completely on the wrong path, first time taking this kind of proof class.