Product of Subset with Union

Theorem
Let $\left({G, \circ}\right)$ be an algebraic structure.

Let $X, Y, Z \subseteq G$.

Then:


 * $X \circ \paren {Y \cup Z} = \paren {X \circ Y} \cup \paren {X \circ Z}$


 * $\paren {Y \cup Z} \circ X = \paren {Y \circ X} \cup \paren {Z \circ X}$

where $X \circ Y$ denotes the subset product of $X$ and $Y$.