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Select the correct answer.

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

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

Answer :

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

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

We'll do it one term at a time:

[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]

[tex]\[
-4x^2 \cdot -7 = 28x^2
\][/tex]

Step 2: Combine the results.

Putting these two results together, we get:

[tex]\[
-12x^3 + 28x^2
\][/tex]

So the simplified form of the expression [tex]\(-4x^2(3x-7)\)[/tex] is:

[tex]\[
\boxed{-12x^3 + 28x^2}
\][/tex]

Therefore, the correct answer is:

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

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