The equation in the image is:

$3(x^2 + y) + (x + 5 + y)$

Let's simplify this step by step:

Step 1: Expand the terms

Expand $3(x^2 + y)$: $3(x^2 + y) = 3x^2 + 3y$

The second term $(x + 5 + y)$ stays as it is for now.

$3x^2 + 3y + (x + 5 + y)$

Step 2: Combine like terms

Group the like terms:

• $3x^2$ (no other $x^2$ terms, so it stays as it is)
• $3y + y = 4y$
• $x$ (no other $x$ terms, so it stays as it is)
• The constant $5$ remains.

$3x^2 + x + 4y + 5$

Final Simplified Expression:

$3x^2 + x + 4y + 5$

Would you like further details or explanations?

Related Questions:

1. How can you factor the simplified expression further, if possible?
2. What are the values of $x$ and $y$ if the equation equals a specific constant, such as 0?
3. Can you graph this equation if given a specific $z$-value?
4. How do you substitute specific values of $x$ and $y$ to calculate results?
5. What techniques are used to simplify expressions with multiple variables?

Tip:

When simplifying expressions, always look for like terms first and remember to distribute multiplication across terms in parentheses!