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------------------------------------------------ Select the correct answer.

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

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

Answer :

To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we can distribute [tex]\(-4x^2\)[/tex] across the elements inside the parentheses. Let's break it down step by step:

1. Identify the terms inside the parentheses:
The expression inside the parentheses is [tex]\(3x - 7\)[/tex].

2. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by the first term, [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by the second term, [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]

3. Combine the results of the distribution:
The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]

Thus, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option D.