To simplify the expression \((r + 2) \cdot (s + 3)\), we can apply the distributive property (also known as the FOIL method in the case of binomials). Here's how the expression is expanded:

\[
(r + 2) \cdot (s + 3) = r \cdot s + r \cdot 3 + 2 \cdot s + 2 \cdot 3
\]

Now, let's perform each multiplication step:

1. \(r \cdot s = rs\)
2. \(r \cdot 3 = 3r\)
3. \(2 \cdot s = 2s\)
4. \(2 \cdot 3 = 6\)

Combining all these terms, we get the expanded expression:

\[
rs + 3r + 2s + 6
\]

So, the simplified form of \((r + 2)(s + 3)\) is:

\[
rs + 3r + 2s + 6
\]

Would you like to ask more questions or need further details?

Here are some related questions you might find interesting:

1. How do you apply the distributive property to expressions with more than two terms?
2. What is the FOIL method, and when is it used?
3. Can you factor the expression \(rs + 3r + 2s + 6\)?
4. How does expanding binomials help in solving algebraic equations?
5. What are some practical applications of expanding and simplifying algebraic expressions?

**Tip:** When expanding expressions, carefully apply the distributive property to ensure all terms are correctly multiplied.

Learn how to simplify the expression (r + 2)(s + 3) using the distributive property (FOIL method for binomials). Step-by-step explanation with multiplication of terms like rs, 3r, 2s, and 6. Suitable for students in Grades 7-9.

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