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

To simplify the expression [tex]$-4x^2(3x-7)$[/tex], you need to distribute [tex]$-4x^2$[/tex] across each term inside the parentheses. Let's break it down step-by-step:

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

- First, distribute [tex]$-4x^2$[/tex] to [tex]$3x$[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]

- Next, distribute [tex]$-4x^2$[/tex] to [tex]$-7$[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]

2. Combine the terms:

After the distribution, you combine the terms you obtained:
[tex]\[
-12x^3 + 28x^2
\][/tex]

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

Therefore, the correct answer is A. [tex]$-12x^3 + 28x^2$[/tex].