1. **State the problem:** Simplify the expression $$(4x^2 + 3x - 5) + (2x^2 - x + 7)$$. 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:** $$4x^2 + 3x - 5 + 2x^2 - x + 7$$ Group like terms: $$(4x^2 + 2x^2) + (3x - x) + (-5 + 7)$$ 4. **Simplify each group:** $$4x^2 + 2x^2 = 6x^2$$ $$3x - x = 2x$$ $$-5 + 7 = 2$$ 5. **Final simplified expression:** $$6x^2 + 2x + 2$$ This is the sum of the two polynomials.