1. **State the problem:** Simplify the expression $3x^2 + x^2$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part unchanged. 3. **Intermediate work:** $$3x^2 + x^2 = (3 + 1)x^2 = 4x^2$$ 4. **Explanation:** Since both terms have the same variable part $x^2$, we add the coefficients $3$ and $1$ to get $4$, so the simplified expression is $4x^2$. **Final answer:** $4x^2$