Question According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x ?(1 point) Responses (2x2+4)(2x2+3) left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x squared plus 3 right parenthesis 4x(x2+2x+3) 4 x left parenthesis x squared plus 2 x plus 3 right parenthesis (2x2+4)(2x−3) left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x minus 3 right parenthesis 4x(4x+5x)

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:

**\(4x(x^2 + 2x + 3)\)**.