1. **State the problem:** Simplify the polynomial expression $2x^3 + 4x^2 + 5x^3 + 6x^2$. 2. **Identify like terms:** Terms with the same variable and exponent can be combined. Here, $2x^3$ and $5x^3$ are like terms, and $4x^2$ and $6x^2$ are like terms. 3. **Combine like terms:** - Combine $2x^3$ and $5x^3$: $$2x^3 + 5x^3 = (2 + 5)x^3 = 7x^3$$ - Combine $4x^2$ and $6x^2$: $$4x^2 + 6x^2 = (4 + 6)x^2 = 10x^2$$ 4. **Write the simplified expression:** $$7x^3 + 10x^2$$ 5. **Explanation:** Combining like terms means adding their coefficients while keeping the variable part the same. This simplifies the expression and makes it easier to work with. **Final answer:** $$7x^3 + 10x^2$$