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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