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The image provides a mathematical problem regarding the use of the binomial expansion and combining like terms. Here's the translated and detailed version of the task:

---

**Summalauskeekkeet, binomin neliökaava ja samanmuotoisten termien yhdistäminen**

Remove the parentheses and simplify the following expression:

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

**Instructions:**
1. Apply the binomial square expansion formula to both binomials.
2. After expansion, combine like terms.

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### Step-by-Step Solution:

1. **Expand the binomials using the square of a sum formula:**
   \[
   (a + b)^2 = a^2 + 2ab + b^2
   \]
   Apply this formula to each binomial.

   - First term: \((3x + 2y)^2\)
     \[
     = (3x)^2 + 2(3x)(2y) + (2y)^2 = 9x^2 + 12xy + 4y^2
     \]

   - Second term: \((2x + 3y)^2\)
     \[
     = (2x)^2 + 2(2x)(3y) + (3y)^2 = 4x^2 + 12xy + 9y^2
     \]

2. **Combine the expanded terms:**
   \[
   (9x^2 + 12xy + 4y^2) + (4x^2 + 12xy + 9y^2)
   \]

   Now, add the like terms:

   - \(9x^2 + 4x^2 = 13x^2\)
   - \(12xy + 12xy = 24xy\)
   - \(4y^2 + 9y^2 = 13y^2\)

3. **Final simplified expression:**
   \[
   13x^2 + 24xy + 13y^2
   \]

---

This is the fully simplified form of the given expression.

Would you like a deeper explanation of any part of the process? Here are some related questions you could explore:

1. How do you expand other types of binomial products?
2. What happens when you expand \((x - y)^2\)?
3. Can the same approach be used to expand \((x + y + z)^2\)?
4. What are some real-world applications of binomial expansions?
5. How do you identify and combine like terms in a complex algebraic expression?

**Tip:** Always start by expanding each binomial separately and then carefully combine like terms to simplify.

Remove the parentheses and simplify the following expression: (3x + 2y)^2 + (2x + 3y)^2

Learn how to expand and simplify the binomials (3x + 2y)^2 + (2x + 3y)^2 using the binomial square formula and combining like terms. Suitable for students in Grades 8-10.

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