Problem on non-empty sets

Question

Assignment:

Let X and Y be non-empty sets. If A₁ and  A₂ are subsets of  X and B₁ and B₂ subsets of Y,  show that (A₁ x B₁) U (A₂ x B₂) = (A₁ U A₂) x (B₁ U B₂).

Provide complete and step by step solution for the question and show calculations and use formulas.