https://file.aiquickdraw.com/mathbot/file/17248177882643g5wr1dj.jpg

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.

Learn how to solve the expression 2y + 3(x - y) + x^2 where x = 3 and y = 5 with a detailed step-by-step solution. This problem covers key algebraic concepts including substitution, simplification, and arithmetic operations. Suitable for students in Grades 7-9.

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