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 first factor out the greatest common factor (GCF) from the original expression.

The original expression is:
\[
4x^3 + 8x^2 + 12x
\]

The GCF of the coefficients (4, 8, and 12) is 4, and the common factor among the terms is \(x\). Therefore, we can factor out \(4x\):

\[
4x(x^2 + 2x + 3)
\]

Now, let's check the provided responses to see which one matches the factored form \(4x(x^2 + 2x + 3)\):

1. **\((2x^2 + 4)(2x^2 + 3)\)**: This does not match.
2. **\((2x^2 + 4)(2x - 3)\)**: This does not match.
3. **\(4x(4x + 5x)\)**: This simplifies to \(4x(9x)\), which does not match.
4. **\(4x(x^2 + 2x + 3)\)**: This matches our factored expression.

Thus, the expression \(4x(x^2 + 2x + 3)\) is equivalent to \(4x^3 + 8x^2 + 12x\).

The correct answer is:
**\(4x(x^2 + 2x + 3)\)**.