To combine like terms in the expression $3x^2 + x + x^2 + y^2$, follow these steps:

Step-by-step Solution:

1. Group the like terms:

   • Terms with $x^2$: $3x^2$ and $x^2$.
   • Terms with $x$: $x$.
   • Terms with $y^2$: $y^2$.

2. Combine coefficients for like terms:

   • $3x^2 + x^2 = 4x^2$.
   • $x$ remains as it is.
   • $y^2$ remains as it is.

3. Write the simplified expression: $4x^2 + x + y^2$

Final Answer:

$4x^2 + x + y^2$

Do you want further details or have any questions?

Related Questions:

1. What are like terms, and how do you identify them?
2. How do coefficients affect the process of combining like terms?
3. Can $x^2$ and $y^2$ ever be combined?
4. How do you approach expressions with multiple variables?
5. What happens if the terms have different exponents?

Tip:

Always arrange the terms in standard order (highest power to lowest) for clarity when simplifying expressions.