According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x

To determine which expression is equivalent to \( 4x^3 + 8x^2 + 12x \) using the Distributive Property, we can start by factoring the expression.

1. **Identify the common factor:** Each term in the polynomial \( 4x^3 + 8x^2 + 12x \) has a common factor of \( 4x \).

2. **Factor out the common factor:**
\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3).
\]

Now, let's check each of the provided response options:

1. \( (2x^2 + 4)(2x^2 + 3) \)
2. \( (2x^2 + 4)(2x - 3) \)
3. \( 4x(4x + 5x) \) — This simplifies to \( 4x(9x) = 36x^2\) which does not match.
4. \( 4x(x^2 + 2x + 3) \) — This matches our factorization.

Based on this analysis, the correct answer is:

**\( 4x(x^2 + 2x + 3) \)**.

Thus, the response that is equivalent to \( 4x^3 + 8x^2 + 12x \) is:

**\( 4x(x^2 + 2x + 3) \)**.