Let's solve the expression provided in the image:

The expression to evaluate is: $2y + 3(x - y) + x^2$ where $x = 3$ and $y = 5$.

Step 1: Substitute the values of $x$ and $y$ into the expression.

$2(5) + 3(3 - 5) + 3^2$

Step 2: Simplify the expression.

• First, calculate $2y$: $2(5) = 10$
• Next, simplify inside the parentheses: $3 - 5 = -2$
• Multiply by 3: $3(-2) = -6$
• Then, compute the square of $x$: $3^2 = 9$

Step 3: Add the results together.

$10 + (-6) + 9$

Step 4: Perform the addition.

$10 - 6 + 9 = 13$

So, the value of the expression is $\boxed{13}$.

Do you have any questions or would you like further details? Here are some related questions you might find interesting:

1. How would the expression change if $y = x$?
2. What is the impact of the square term $x^2$ on the overall expression?
3. Can you factor the expression to simplify it before substituting the values?
4. What if the expression had a division instead of addition—how would that affect the steps?
5. How would you handle this expression if it were part of a larger equation?

Tip: Squaring a number, as in $x^2$, always results in a non-negative value, which can significantly impact the final result of an expression.