To find the expression equivalent to \( 4x^3 + 8x^2 + 12x \) using the Distributive Property, we can start by factoring out the greatest common factor (GCF) from the terms in the expression.
The GCF of \( 4x^3, 8x^2, \) and \( 12x \) is \( 4x \).
Now, we can factor \( 4x \) out of the expression:
\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)
\]
Now, let's evaluate the answer options provided:
1. \( (2x^2 + 4)(2x^2 + 3) \)
2. \( 4x(4x + 5x) \)
3. \( (2x^2 + 4)(2x - 3) \)
4. \( 4x(x^2 + 2x + 3) \) — This is the correct option.
Given the expression \( 4x(x^2 + 2x + 3) \) matches our factored form directly, the correct answer is:
**4x(x² + 2x + 3)**