1. **State the problem:** Simplify the expression $$(2v^2 - 9v + 9) + (4v^2 - 8v + 5) - (-7v^2 + 5v + 5)$$ 2. **Apply the distributive property:** Remove parentheses and change signs for the last group because of the minus sign: $$2v^2 - 9v + 9 + 4v^2 - 8v + 5 + 7v^2 - 5v - 5$$ 3. **Group like terms:** $$(2v^2 + 4v^2 + 7v^2) + (-9v - 8v - 5v) + (9 + 5 - 5)$$ 4. **Add coefficients:** $$\cancel{2v^2} + \cancel{4v^2} + 7v^2 = 13v^2$$ $$-9v - 8v - 5v = -22v$$ $$9 + 5 - 5 = 9$$ 5. **Write the simplified expression:** $$13v^2 - 22v + 9$$ **Final answer:** $$13v^2 - 22v + 9$$