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

Question

4
𝑥
3
+
8
𝑥
2
+
12
𝑥
?(1 point)
Responses

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

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

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

(2x2+4)(2x−3)

Answer 1

To find an expression equivalent to \(4x^3 + 8x^2 + 12x\) using the Distributive Property, we can factor out the common term from each part of the expression.

1. Identify the common factor:

   • Each term \(4x^3\), \(8x^2\), and \(12x\) has a common factor of \(4x\).

2. Factor out \(4x\): \[ 4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3) \]

Now let's look at the answer choices:

1. \(4x(x^2 + 2x + 3)\) - This matches our factored expression.
2. \((2x^2 + 4)(2x^2 + 3)\) - This is not equivalent.
3. \(4x(4x + 5x)\) - This equals \(4x(9x) = 36x^2\), which is not equivalent.
4. \((2x^2 + 4)(2x - 3)\) - This is not equivalent.

The correct equivalent expression according to the Distributive Property is: \[ 4x(x^2 + 2x + 3) \]