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 :

Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step by step.

1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:

The given expression is:
[tex]\[
-4x^2(3x - 7)
\][/tex]

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

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

4. Combine the results of the distributions:
[tex]\[
-12x^3 + 28x^2
\][/tex]

So, the simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]

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

This matches option D in the given choices:

D. [tex]\(-12x^3 + 28x^2\)[/tex]

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