1. **State the problem:** Expand and simplify the expression $$(4x - 3)(2x - 5)$$. 2. **Recall the distributive property (FOIL method):** To multiply two binomials, multiply each term in the first binomial by each term in the second binomial. 3. **Apply FOIL:** - First: $4x \times 2x = 8x^2$ - Outer: $4x \times (-5) = -20x$ - Inner: $-3 \times 2x = -6x$ - Last: $-3 \times (-5) = 15$ 4. **Write the expanded form:** $$8x^2 - 20x - 6x + 15$$ 5. **Combine like terms:** $$8x^2 - \cancel{20x} - \cancel{6x} + 15 = 8x^2 - 26x + 15$$ 6. **Final answer:** $$8x^2 - 26x + 15$$