1. **State the problem:** Expand the expression $ (5x + 2y)(3x - 2y) $. 2. **Apply the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second parenthesis. $ (5x)(3x) + (5x)(-2y) + (2y)(3x) + (2y)(-2y) $ 3. **Calculate each multiplication:** $ 15x^2 - 10xy + 6xy - 4y^2 $ 4. **Combine like terms:** $ 15x^2 - 4xy - 4y^2 $ 5. **Final answer:** $$\boxed{15x^2 - 4xy - 4y^2}$$