To simplify the expression $(x + 3)(x^2 - 3x + 9)$, we’ll use the distributive property (also known as the FOIL method for binomials).

Step-by-Step Solution:

1. Distribute $x$ to each term in $x^2 - 3x + 9$: $x \cdot x^2 = x^3$ $x \cdot (-3x) = -3x^2$ $x \cdot 9 = 9x$

   So, the terms from distributing $x$ are: $x^3 - 3x^2 + 9x$.

2. Distribute $3$ to each term in $x^2 - 3x + 9$: $3 \cdot x^2 = 3x^2$ $3 \cdot (-3x) = -9x$ $3 \cdot 9 = 27$

   So, the terms from distributing $3$ are: $3x^2 - 9x + 27$.

3. Combine all terms: $x^3 - 3x^2 + 9x + 3x^2 - 9x + 27$

4. Combine like terms:

   • $x^3$ (no like terms here)
   • $-3x^2 + 3x^2 = 0$
   • $9x - 9x = 0$
   • $+27$

   This simplifies to: $x^3 + 27$

Final Answer:

The simplified expression is: $x^3 + 27$

Answer Choice:

The correct answer is:

• $x^3 + 27$

Would you like further clarification, or have any additional questions?

Related Questions:

1. How can we apply the distributive property to other polynomial products?
2. What is the FOIL method, and when is it most effective?
3. How do we identify and combine like terms in polynomial expressions?
4. Can we use other methods to simplify $(x + 3)(x^2 - 3x + 9)$?
5. How does recognizing patterns like the sum of cubes help in factoring?

Tip:

When simplifying expressions, always look for opportunities to combine like terms to reduce the expression to its simplest form.