High School

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

Answer :

To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], you need to distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses. Let's go through this step-by-step:

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

[tex]\[
-4x^2 \cdot 3x = -12x^{2+1} = -12x^3
\][/tex]

2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:

[tex]\[
-4x^2 \cdot (-7) = 28x^{2+0} = 28x^2
\][/tex]

3. Combine the results:

The two terms resulting from the distribution are [tex]\(-12x^3\)[/tex] and [tex]\(28x^2\)[/tex]. Putting these together, we get:

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

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