To find the expression equivalent to $4x^3 + 8x^2 + 12x$ using the Distributive Property, we need to factor out the greatest common factor (GCF) from each term.

1. The expression is $4x^3 + 8x^2 + 12x$.
2. The GCF of the terms $4x^3$, $8x^2$, and $12x$ is $4x$.
3. Factoring $4x$ from each term: $4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)$

So, the correct expression equivalent to $4x^3 + 8x^2 + 12x$ is:

$4x(x^2 + 2x + 3)$

This matches the second option:

• $4x(x^2 + 2x + 3)$

Do you want more details or have any questions?

Here are some related questions:

1. What is the Distributive Property, and how does it work in algebra?
2. How do you factor out the greatest common factor in an expression?
3. What are the steps to simplify an algebraic expression?
4. How do you identify the GCF in a polynomial expression?
5. Can the expression $4x^3 + 8x^2 + 12x$ be factored further?
6. What are some common mistakes when applying the Distributive Property?
7. How does factoring help in solving algebraic equations?
8. What is the importance of recognizing patterns in algebraic expressions?

Tip: When factoring, always start by identifying the greatest common factor to simplify the expression first.