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The problem in the image asks to expand the expression \( (2x + y)(5x + 3y) \).

Let me guide you through the process of expanding this:

### Step-by-step expansion:

1. Use the distributive property (also known as FOIL for binomials) to expand:
\[
(2x + y)(5x + 3y) = 2x(5x + 3y) + y(5x + 3y)
\]

2. Distribute each term:
\[
= (2x \cdot 5x) + (2x \cdot 3y) + (y \cdot 5x) + (y \cdot 3y)
\]

3. Simplify each product:
\[
= 10x^2 + 6xy + 5xy + 3y^2
\]

4. Combine like terms:
\[
= 10x^2 + (6xy + 5xy) + 3y^2
\]
\[
= 10x^2 + 11xy + 3y^2
\]

### Final Answer:
\[
10x^2 + 11xy + 3y^2
\]

Would you like more details or have any questions? Here are five related questions to further explore this topic:

1. How do you apply the distributive property when expanding binomials?
2. What is the FOIL method, and how does it apply to binomial expansion?
3. How can you recognize and combine like terms in an expression?
4. What is the significance of the terms \( x^2 \), \( xy \), and \( y^2 \) in polynomial expressions?
5. How would the expansion change if one or both of the binomials were altered (e.g., \( (2x - y)(5x + 3y) \))?

**Tip:** When expanding binomials, always distribute each term in the first binomial to every term in the second binomial to ensure no terms are missed.

Learn how to expand the expression (2x + y)(5x + 3y) using the distributive property. This algebra problem involves binomial expansion and polynomial combination, suitable for students in Grades 7-9.

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