To expand the expression $(4x - 5)(x^2 + 4x + 1)$, we'll apply the distributive property (also known as the FOIL method when dealing with binomials). This involves distributing each term in $4x - 5$ to every term in $x^2 + 4x + 1$.

Step-by-step solution:

$(4x - 5)(x^2 + 4x + 1)$

1. Distribute $4x$: $4x \cdot (x^2 + 4x + 1) = 4x^3 + 16x^2 + 4x$

2. Distribute $-5$: $-5 \cdot (x^2 + 4x + 1) = -5x^2 - 20x - 5$

3. Combine like terms: $4x^3 + (16x^2 - 5x^2) + (4x - 20x) - 5$

   This simplifies to: $4x^3 + 11x^2 - 16x - 5$

Thus, the expanded polynomial in standard form is:

$\boxed{4x^3 + 11x^2 - 16x - 5}$

---

Would you like more details or have any questions on this?

Here are 5 related questions to practice:

1. Expand $(3x - 2)(x^2 + 5x + 3)$.
2. Expand and simplify $(2x + 3)(x^2 - x + 4)$.
3. Factor $4x^3 + 11x^2 - 16x - 5$ back into its factors.
4. How does the FOIL method apply to binomials?
5. What are the standard forms of polynomials?

Tip: When expanding, always combine like terms to simplify the expression!