High School

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Select the correct answer.

Simplify the expression [tex]-4x^2(3x-7)[/tex].

A. [tex]-12x^3-28[/tex]
B. [tex]-12x^3+28[/tex]
C. [tex]-12x^3-28x^2[/tex]
D. [tex]-12x^3+28x^2[/tex]

Answer :

To simplify the expression [tex]\(-4 x^2(3 x-7)\)[/tex], we need to apply the distributive property, which means we multiply each term inside the parentheses by [tex]\(-4 x^2\)[/tex].

Here are the steps broken down:

1. Multiply [tex]\(-4 x^2\)[/tex] by [tex]\(3 x\)[/tex]:
[tex]\[
-4 x^2 \cdot 3 x = -12 x^3
\][/tex]

2. Multiply [tex]\(-4 x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4 x^2 \cdot -7 = 28 x^2
\][/tex]

Putting these results together, you get the simplified expression:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]

So the correct answer is:
[tex]\[
\boxed{-12 x^3 + 28 x^2}
\][/tex]

Therefore, the correct choice is:
D. [tex]\(-12 x^3 + 28 x^2\)[/tex]

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