Let's expand the expression \((3x + 8)(x + 3)\) using the distributive property (FOIL method).

\[
(3x + 8)(x + 3) = 3x(x) + 3x(3) + 8(x) + 8(3)
\]

Now, let's calculate each term:

\[
3x(x) = 3x^2
\]
\[
3x(3) = 9x
\]
\[
8(x) = 8x
\]
\[
8(3) = 24
\]

Now, add all the terms together:

\[
3x^2 + 9x + 8x + 24
\]

Combine like terms:

\[
3x^2 + (9x + 8x) + 24 = 3x^2 + 17x + 24
\]

So, the expanded form of \((3x + 8)(x + 3)\) is:

\[
3x^2 + 17x + 24
\]

Would you like more details on any part of this solution?

Here are 5 related questions to explore further:
1. How would the expression change if one of the terms was negative?
2. Can you factor \(3x^2 + 17x + 24\) back into its original form?
3. What happens if you substitute \(x = 2\) into the expanded expression?
4. How can you apply the FOIL method to three binomials?
5. What is the geometric interpretation of multiplying two binomials?

**Tip:** Always combine like terms after distributing to simplify the expression further.

Learn how to expand and simplify the binomial expression (3x+8)(x+3) using the distributive property (FOIL method). This solution provides a step-by-step explanation and combines like terms, making it ideal for students in Grades 7-9 who are learning algebraic methods for multiplying binomials.

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