To solve this, follow these steps:

1. Start with the expression: $x^2 + 3$.

2. Add 1 to the expression: $x^2 + 3 + 1 = x^2 + 4$

3. Multiply the result by 3: $3 \times (x^2 + 4) = 3x^2 + 12$

So, after adding 1 and multiplying by 3, the expression becomes $3x^2 + 12$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you factor the expression $3x^2 + 12$?
2. What is the derivative of $3x^2 + 12$ with respect to $x$?
3. How do you find the roots of $3x^2 + 12 = 0$?
4. What is the vertex form of the quadratic $3x^2 + 12$?
5. How do you graph the equation $y = 3x^2 + 12$?
6. What are the properties of the quadratic function $3x^2 + 12$?
7. How does the value of 3 affect the parabola of $y = 3x^2 + 12$ compared to $y = x^2 + 4$?
8. What is the range of the function $y = 3x^2 + 12$?

Tip: Always perform operations in the correct order (following the order of operations: parentheses, exponents, multiplication and division, addition and subtraction).