To simplify the expression $(x + 3)(x^3 - x + 1)$, we will use the distributive property (also known as the FOIL method in the case of binomials) to multiply each term in the first parenthesis by each term in the second parenthesis.

Step-by-Step Solution:

1. Distribute $x$: $x \cdot (x^3 - x + 1) = x^4 - x^2 + x$

2. Distribute $3$: $3 \cdot (x^3 - x + 1) = 3x^3 - 3x + 3$

3. Combine like terms: $x^4 + 3x^3 - x^2 - 2x + 3$

Final Simplified Expression:

$\boxed{x^4 + 3x^3 - x^2 - 2x + 3}$

Would you like further details or have any questions?

Related Questions:

1. How do you use the distributive property to multiply polynomials?
2. What are like terms, and how do you combine them?
3. How can you factor the resulting polynomial?
4. What is the degree of a polynomial, and what is it for the final expression here?
5. How do you apply polynomial multiplication to solve real-world problems?

Tip:

When simplifying polynomials, always ensure that all like terms are combined to reach the most simplified form!