1. The problem is to multiply the expressions $(2\sqrt{2} - \sqrt{5}) \cdot (\sqrt{2} + \sqrt{5})$ using the difference of squares formula. 2. Recall the difference of squares formula: $ (a - b)(a + b) = a^2 - b^2 $. This formula applies when the two binomials are conjugates. 3. Identify $a = 2\sqrt{2}$ and $b = \sqrt{5}$. 4. Apply the formula: $$ (2\sqrt{2} - \sqrt{5})(\sqrt{2} + \sqrt{5}) = (2\sqrt{2})^2 - (\sqrt{5})^2 $$ 5. Calculate each square: $$ (2\sqrt{2})^2 = 2^2 \times (\sqrt{2})^2 = 4 \times 2 = 8 $$ $$ (\sqrt{5})^2 = 5 $$ 6. Substitute back: $$ 8 - 5 = 3 $$ 7. Therefore, the product is $3$.