1. **State the problem:** Simplify the expression $5x^2 + 8x + 3x^2$. 2. **Combine like terms:** Like terms are terms that have the same variable raised to the same power. Here, $5x^2$ and $3x^2$ are like terms. 3. **Add the coefficients of like terms:** $$5x^2 + 3x^2 = (5 + 3)x^2 = 8x^2$$ 4. **Rewrite the expression:** $$8x^2 + 8x$$ 5. **Final simplified expression:** $$\boxed{8x^2 + 8x}$$ This means the original expression simplifies to $8x^2 + 8x$ by combining like terms.