1. **State the problem:** Simplify the expression $$(9x^2 + 8x - 8) + (-9x^2 - 3x - 9) - (-7x^2 + 4x + 7).$$ 2. **Write the expression clearly:** $$9x^2 + 8x - 8 + (-9x^2 - 3x - 9) - (-7x^2 + 4x + 7)$$ 3. **Distribute the minus sign to the last parentheses:** $$9x^2 + 8x - 8 - 9x^2 - 3x - 9 + 7x^2 - 4x - 7$$ 4. **Group like terms:** - For $x^2$: $$9x^2 - 9x^2 + 7x^2$$ - For $x$: $$8x - 3x - 4x$$ - Constants: $$-8 - 9 - 7$$ 5. **Simplify each group:** - $x^2$ terms: $$9x^2 - 9x^2 + 7x^2 = \cancel{9x^2} - \cancel{9x^2} + 7x^2 = 7x^2$$ - $x$ terms: $$8x - 3x - 4x = 8x - \cancel{3x} - \cancel{4x} = 8x - 7x = 1x = x$$ - Constants: $$-8 - 9 - 7 = -8 - 16 = -24$$ 6. **Write the simplified expression:** $$7x^2 + x - 24$$ **Final answer:** $$7x^2 + x - 24$$