1. **State the problem:** We want to use the box method to distribute and simplify the product $$(5x - 3)(-x - 2)$$. 2. **Explain the box method:** The box method involves creating a grid where each term of the first binomial is placed along the top (columns) and each term of the second binomial is placed along the side (rows). Then, multiply each pair of terms and place the result in the corresponding box. 3. **Set up the box:** - Columns: $5x$, $-3$ - Rows: $-x$, $-2$ 4. **Fill in the boxes by multiplying:** - Top-left box: $5x \times (-x) = -5x^2$ - Top-right box: $-3 \times (-x) = 3x$ - Bottom-left box: $5x \times (-2) = -10x$ - Bottom-right box: $-3 \times (-2) = 6$ 5. **Write the box:** | | $5x$ | $-3$ | |-------|--------|-------| | $-x$ | $-5x^2$| $3x$ | | $-2$ | $-10x$ | $6$ | 6. **Combine like terms:** $$-5x^2 + 3x - 10x + 6 = -5x^2 - 7x + 6$$ 7. **Final answer:** $$\boxed{-5x^2 - 7x + 6}$$