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To find an expression equivalent to \(4x^3 + 8x^2 + 12x\) using the Distributive Property, we can factor out the greatest common factor (GCF) from the expression.
The GCF of \(4x^3\), \(8x^2\), and \(12x\) is \(4x\).
Now we can factor \(4x\) out of the expression:
\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)
\]
Thus, the equivalent expression is:
\[
4x(x^2 + 2x + 3)
\]
Looking at the responses provided:
- \((2x^2 + 4)(2x^2 + 3)\)
- **\(4x(x^2 + 2x + 3)\)** (This is the correct answer)
- \((2x^2 + 4)(2x - 3)\)
- \(4x(4x + 5x)\)
The correct response is:
**\(4x(x^2 + 2x + 3)\)**.