1. **State the problem:** Simplify the expression $(-7k + 6) + (4k + 5)(-5k + 5)$. 2. **Use the distributive property:** Expand the product $(4k + 5)(-5k + 5)$. $$ (4k)(-5k) + (4k)(5) + (5)(-5k) + (5)(5) = -20k^2 + 20k - 25k + 25 $$ 3. **Combine like terms inside the product:** $$ -20k^2 + (20k - 25k) + 25 = -20k^2 - 5k + 25 $$ 4. **Add the first term $(-7k + 6)$ to the expanded product:** $$ (-7k + 6) + (-20k^2 - 5k + 25) $$ 5. **Combine like terms:** - For $k^2$: $-20k^2$ - For $k$: $-7k - 5k = -12k$ - For constants: $6 + 25 = 31$ 6. **Final simplified expression:** $$ \boxed{-20k^2 - 12k + 31} $$