1. **State the problem:** Expand the expression $ (5x - 2y)(3x + 4y) $. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $ (a + b)(c + d) = ac + ad + bc + bd $. 3. **Apply the formula:** $$ (5x - 2y)(3x + 4y) = 5x \cdot 3x + 5x \cdot 4y - 2y \cdot 3x - 2y \cdot 4y $$ 4. **Multiply each term:** $$ = 15x^2 + 20xy - 6xy - 8y^2 $$ 5. **Combine like terms:** $$ 20xy - 6xy = 14xy $$ 6. **Final expanded form:** $$ 15x^2 + 14xy - 8y^2 $$ This is the expanded expression of the given product.