Cartesian Product of Unions

Theorem
$$\left({S_1 \cup S_2}\right) \times \left({T_1 \cup T_2}\right) = \left({S_1 \times T_1}\right) \cup \left({S_2 \times T_2}\right) \cup \left({S_1 \times T_2}\right) \cup \left({S_2 \times T_1}\right) $$