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To find an expression that is equivalent to \(4x^3 + 8x^2 + 12x\) using the Distributive Property, we can first factor out the common term in the expression.
Looking at the expression:
\[
4x^3 + 8x^2 + 12x
\]
We can factor out \(4x\):
\[
4x(x^2 + 2x + 3)
\]
Now, let's compare this with the given response options:
1. \((2x^2 + 4)(2x^2 + 3)\)
2. \(4x(x^2 + 2x + 3)\)
3. \((2x^2 + 4)(2x - 3)\)
4. \(4x(4x + 5x)\)
The correct expression that matches our factored form is:
\[
4x(x^2 + 2x + 3)
\]
So the answer is:
**\(4x(x^2 + 2x + 3)\)**.