1. **Problem:** Simplify the expression by combining like terms: $$(2x^3 - 3x^2 + 4x) + (-3x^3 + 5x^2 - 2x)$$ 2. **Formula and rules:** To combine like terms, add or subtract the coefficients of terms with the same variable and exponent. 3. **Step-by-step simplification:** - Combine $x^3$ terms: $2x^3 + (-3x^3) = (2 - 3)x^3 = -1x^3$ - Combine $x^2$ terms: $-3x^2 + 5x^2 = (-3 + 5)x^2 = 2x^2$ - Combine $x$ terms: $4x + (-2x) = (4 - 2)x = 2x$ 4. **Final simplified expression:** $$-x^3 + 2x^2 + 2x$$ This is the combined expression with like terms added together.