1. **State the problem:** Simplify the expression $$(-5t^2 - 4t + 1) + (-3t^2 + 7)$$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the same variable raised to the same power. 3. **Combine like terms:** - Combine the $t^2$ terms: $$-5t^2 + (-3t^2) = -5t^2 - 3t^2$$ - Combine the $t$ terms: $$-4t$$ (no like term in second polynomial) - Combine the constants: $$1 + 7$$ 4. **Simplify each group:** $$-5t^2 - 3t^2 = (-5 - 3)t^2 = -8t^2$$ $$1 + 7 = 8$$ 5. **Write the simplified polynomial:** $$-8t^2 - 4t + 8$$ **Final answer:** $$\boxed{-8t^2 - 4t + 8}$$