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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]

Answer :

To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property. This property allows us to multiply each term inside the parentheses by the term outside the parentheses.

Here are the steps:

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

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

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

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

3. Combine the results from steps 1 and 2:

[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]