To find the product $(x + 3)(x^2 - 3x + 9)$, we can use the distributive property (also known as the FOIL method for binomials). Here, we'll distribute each term in the first expression $x + 3$ to each term in the second expression $x^2 - 3x + 9$.

Step-by-Step Solution:

1. Distribute $x$ to each term in the second polynomial: $x \cdot (x^2 - 3x + 9) = x \cdot x^2 - x \cdot 3x + x \cdot 9$ Simplifying this, we get: $x^3 - 3x^2 + 9x$

2. Distribute $3$ to each term in the second polynomial: $3 \cdot (x^2 - 3x + 9) = 3 \cdot x^2 - 3 \cdot 3x + 3 \cdot 9$ Simplifying this, we get: $3x^2 - 9x + 27$

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

4. Simplify by combining like terms: $x^3 + 0x^2 + 0x + 27$ So the final simplified expression is: $x^3 + 27$

Final Answer:

$(x + 3)(x^2 - 3x + 9) = x^3 + 27$

Would you like more details or have any questions about the solution?

Here are 5 related questions to further your understanding:

1. How do you factorize the expression $x^3 + 27$?
2. What is the result of multiplying $(x - 2)(x^2 + 2x + 4)$?
3. How does the distributive property work with three or more terms?
4. What happens if you expand $(x + 3)^3$?
5. How do you simplify the expression $(2x + 5)(x^2 - 3x + 2)$?

Tip: When multiplying polynomials, always distribute each term from the first polynomial to every term in the second polynomial to ensure all possible products are accounted for.