https://file.aiquickdraw.com/mathbot/file/1726968117078oh3oshge.jpg

I can see that the image contains a worksheet with algebraic expressions that have been factored. Let me guide you through the solutions step by step.

The key exercise I can see is asking you to factor algebraic expressions of the form \( (x + y)^2 \) and perform certain operations on them.

### Let’s analyze a few of the problems visible:

1. **Problem 1:**
   \[
   2(x + y)^2 + 9(x + y) - 5 = 2
   \]
   This equation seems to be a quadratic in \( (x + y) \). The correct approach here is:
   - Let \( z = x + y \), turning it into a standard quadratic equation.
   - Solve for \( z \) using factoring or the quadratic formula.
   - Substitute back \( x + y \) to get the final expression.

2. **Problem 2:**
   \[
   3(x + y)^2 - 13(x + y) + 4 = 4
   \]
   Similar to problem 1, this is a quadratic equation where we let \( z = x + y \), and simplify the equation as:
   \[
   3z^2 - 13z + 4 = 4
   \]
   Subtracting 4 from both sides:
   \[
   3z^2 - 13z = 0
   \]
   Then solve for \( z \) by factoring or using the quadratic formula.

3. **Problem 3:**
   \[
   3(x + y)^2 - 4(x + y) - 4 = 3
   \]
   Again, substitute \( z = x + y \):
   \[
   3z^2 - 4z - 4 = 3
   \]
   Subtracting 3 from both sides:
   \[
   3z^2 - 4z - 7 = 0
   \]
   Solve the quadratic equation to get the factors.

Would you like me to provide detailed solutions for any specific questions from the image, or go over the factoring process for these equations?

### 5 Related Questions:
1. How do you factor quadratic equations like \( 2(x + y)^2 + 9(x + y) - 5 = 2 \)?
2. What is the quadratic formula and when do you use it?
3. How do you solve equations by completing the square?
4. How do you substitute a variable to simplify complex algebraic equations?
5. Can you explain how to solve equations where a squared term is involved?

**Tip:** When solving quadratic equations, always try factoring first before using the quadratic formula—it can save time.

Factor and solve quadratic equations involving expressions like (x + y)^2, such as 2(x + y)^2 + 9(x + y) - 5 = 2.

Learn how to solve quadratic equations with expressions like (x + y)^2 using factoring and the quadratic formula. This topic covers key algebraic concepts, suitable for students in Grades 7-9.

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