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Bot GPT 4-o mini To determine which expression is equivalent to \( 4x^3 + 8x^2 + 12x \) using the Distributive Property, we can factor out the greatest common factor from the expression.
The expression \( 4x^3 + 8x^2 + 12x \) has a common factor of \( 4x \). Factoring \( 4x \) out of the expression gives:
\[
4x(x^2 + 2x + 3)
\]
Now, let's compare this with the options provided:
1. \((2x^2 + 4)(2x - 3)\)
2. \(4x(x^2 + 2x + 3)\)
3. \(4x(4x + 5x)\)
4. \((2x^2 + 4)(2x^2 + 3)\)
The correct choice is:
**\(4x(x^2 + 2x + 3)\)**
So the answer is **\( 4x(x^2 + 2x + 3) \)**.