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]
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]