According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x

Question

?(1 point)
Responses

(2x2+4)(2x−3)
left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x minus 3 right parenthesis

4x(x2+2x+3)
4 x left parenthesis x squared plus 2 x plus 3 right parenthesis

4x(4x+5x)
4 x left parenthesis 4 x plus 5 x right parenthesis

(2x2+4)(2x2+3)
left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x squared plus 3 right parenthesis

Answer 1

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