$A \cap \cup_{\alpha \in \Lamda} B_{\alpha} = \cup_{\alpha \in \Lamda} A \cap B_{\alpha}$ ?

[thin ore]

$A \cap \cup_{\alpha \in \Lambda} B_{\alpha} = \cup_{\alpha \in \Lambda} A \cap B_{\alpha}$

I am trying to prove it and this is how I did. But I am not sure this is correct. can someone correct me?

[astral arrow]

Odd_the_Wolf