1. **State the problem:** Simplify the expression $$(3x - 2)(5x - 2)$$. 2. **Use the distributive property (FOIL method) to expand:** $$ (3x - 2)(5x - 2) = 3x \cdot 5x + 3x \cdot (-2) + (-2) \cdot 5x + (-2) \cdot (-2) $$ 3. **Calculate each term:** $$ 3x \cdot 5x = 15x^2 $$ $$ 3x \cdot (-2) = -6x $$ $$ (-2) \cdot 5x = -10x $$ $$ (-2) \cdot (-2) = 4 $$ 4. **Combine like terms:** $$ 15x^2 - 6x - 10x + 4 = 15x^2 - 16x + 4 $$ 5. **Final simplified expression:** $$ \boxed{15x^2 - 16x + 4} $$ This is the expanded and simplified form of the product of the two binomials.