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To solve the problem, we need to multiply the two expressions given: \( (x^2 + 2x + 1)(x - 3) \).

We will use the distributive property (FOIL method), where each term in the first expression is multiplied by each term in the second expression:

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

### Step-by-step:

1. **Multiply \( x^2 \) by both terms in \( (x - 3) \):**
   \[
   x^2 \cdot x = x^3
   \]
   \[
   x^2 \cdot (-3) = -3x^2
   \]

2. **Multiply \( 2x \) by both terms in \( (x - 3) \):**
   \[
   2x \cdot x = 2x^2
   \]
   \[
   2x \cdot (-3) = -6x
   \]

3. **Multiply \( 1 \) by both terms in \( (x - 3) \):**
   \[
   1 \cdot x = x
   \]
   \[
   1 \cdot (-3) = -3
   \]

### Combine all terms:

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

Simplifying:

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

\[
x^3 - x^2 - 5x - 3
\]

### Final answer:
The product is \( x^3 - x^2 - 5x - 3 \).

Therefore, the correct answer is **Option D**.

---

Would you like a further breakdown of the steps or another explanation?

Here are 5 related questions to explore:
1. How do you factor a polynomial like \( x^3 - x^2 - 5x - 3 \)?
2. What is the degree of the polynomial \( x^3 - x^2 - 5x - 3 \)?
3. How would you solve \( x^3 - x^2 - 5x - 3 = 0 \)?
4. What happens if you multiply \( (x^2 + 2x + 1) \) by a different binomial?
5. Can the expression \( (x^2 + 2x + 1)(x - 3) \) be expanded faster using another method?

**Tip**: When expanding polynomials, ensure each term is correctly multiplied and carefully combine like terms to avoid errors.

Find the product of (x^2 + 2x + 1)(x - 3).

Learn how to find the product of two polynomials, (x^2 + 2x + 1)(x - 3), using the distributive property (FOIL method). Follow a detailed solution with key algebraic concepts and clear explanations. This problem is ideal for students in Grades 9-11.

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