https://file.aiquickdraw.com/mathbot/file/1726414487936y0f2s6ho.jpg

The expression to factorize is:

\[
(x + y)^2 + 3(x + y)
\]

### Step-by-Step Factorization:

1. **Recognize the common factor**: Both terms in the expression contain \((x + y)\). So, factor \((x + y)\) from both terms.

\[
(x + y)\left[(x + y) + 3\right]
\]

2. **Simplify the expression inside the parentheses**:

\[
(x + y)(x + y + 3)
\]

Thus, the factorized form of \((x + y)^2 + 3(x + y)\) is:

\[
(x + y)(x + y + 3)
\]

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Would you like further clarification or details?

Here are some related questions for deeper exploration:

1. How would you factor a cubic expression involving \((x + y)\)?
2. What happens if we add a constant term to the original expression? How would you factor it then?
3. Can this method be applied to more complex binomials, such as \((x - y)\) or \((x + 2y)\)?
4. How does the distributive property help in factorization?
5. Can you expand the factorized form to verify the original expression?

**Tip**: Always look for common terms in factorization to simplify expressions early in the process.

Learn how to factor the algebraic expression (x + y)^2 + 3(x + y) step-by-step. This problem involves recognizing common factors and using the distributive property to simplify the expression. Ideal for students in Grades 9-10.

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