To expand and simplify $(x + 3)(x - 3)(2x + 1)$, we can approach it step-by-step:

Step 1: Expand $(x + 3)(x - 3)$

The expression $(x + 3)(x - 3)$ is a difference of squares: $(x + 3)(x - 3) = x^2 - 9$

Step 2: Substitute and Expand with $(2x + 1)$

Now we need to expand $(x^2 - 9)(2x + 1)$.

Using the distributive property: $(x^2 - 9)(2x + 1) = x^2 \cdot 2x + x^2 \cdot 1 - 9 \cdot 2x - 9 \cdot 1$

Expanding each term:

1. $x^2 \cdot 2x = 2x^3$
2. $x^2 \cdot 1 = x^2$
3. $-9 \cdot 2x = -18x$
4. $-9 \cdot 1 = -9$

Step 3: Combine Terms

Now, put it all together: $2x^3 + x^2 - 18x - 9$

Final Answer

$2x^3 + x^2 - 18x - 9$

Would you like more details on any step?

Here are five related questions to expand your understanding:

1. What is the difference of squares, and how is it generally applied?
2. How do you approach expanding expressions with three or more terms?
3. How can factoring simplify polynomial expressions?
4. How would this change if we added or subtracted an additional term?
5. How can these techniques apply to higher-degree polynomials?

Tip: Practice using the distributive property with different types of polynomials to improve accuracy and speed in expansion tasks.