According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x
?(1 point)
Responses
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)(2x−3)
left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x minus 3 right parenthesis
(2x2+4)(2x2+3)
The Distributive Property expresses the idea that when a number multiplies a sum, you can distribute the multiplication to each addend within the parenthesis. Using the Distributive Property, the expression \( 4x^3 + 8x^2 + 12x \) can be factored by taking out the common factor of 4x from each term. Here's how you do it:
\( 4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3) \)
So, the equivalent expression using the Distributive Property is:
\( 4x(x^2 + 2x + 3) \)
Therefore, the correct response from the given options is:
4x(x^2 + 2x + 3)
OR
4 x left parenthesis x squared plus 2 x plus 3 right parenthesis