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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)

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