The expression \((2x + 1)(3x^2 + 3x - 2)\) represents the multiplication of two binomials. Let's expand this expression step by step.

### Step 1: Distribute each term of the first binomial to every term of the second binomial.

\[
(2x + 1)(3x^2 + 3x - 2) = 2x(3x^2 + 3x - 2) + 1(3x^2 + 3x - 2)
\]

### Step 2: Distribute \(2x\) to each term in the second binomial:

\[
2x(3x^2) + 2x(3x) + 2x(-2) = 6x^3 + 6x^2 - 4x
\]

### Step 3: Distribute \(1\) to each term in the second binomial:

\[
1(3x^2) + 1(3x) + 1(-2) = 3x^2 + 3x - 2
\]

### Step 4: Combine all the terms together:

\[
6x^3 + 6x^2 - 4x + 3x^2 + 3x - 2
\]

### Step 5: Combine like terms:

\[
6x^3 + (6x^2 + 3x^2) + (-4x + 3x) - 2 = 6x^3 + 9x^2 - x - 2
\]

### Final Answer:
\[
\boxed{6x^3 + 9x^2 - x - 2}
\]

Would you like any further explanation or details?

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Here are 8 related questions you might find useful:

1. How do you factor a cubic polynomial like \(6x^3 + 9x^2 - x - 2\)?
2. What are the roots of the polynomial \(6x^3 + 9x^2 - x - 2\)?
3. How do you expand binomials using the FOIL method?
4. What is the difference between expanding and factoring polynomials?
5. How can you apply the distributive property in algebra?
6. What are common mistakes to avoid when expanding binomials?
7. How do you simplify polynomials after expansion?
8. What is the significance of combining like terms in algebra?

**Tip:** When expanding binomials, carefully distribute each term to avoid missing any products, which is a common mistake.

Learn how to expand the expression (2x + 1)(3x^2 + 3x - 2) using the FOIL method with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomials and binomial expansion. Suitable for students in Grades 9-12.

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