College

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], follow these steps:

1. Distribute the [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
This means you multiply [tex]\(-4x^2\)[/tex] by both [tex]\(3x\)[/tex] and [tex]\(-7\)[/tex].

2. Calculate the products:
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = +28x^2
\][/tex]

3. Combine the terms to get the simplified expression:
- Combine the results from the multiplication steps:
[tex]\[
-12x^3 + 28x^2
\][/tex]

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