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

Answer :

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

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

- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]

- Second, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]

2. Combine the results.

- Put the two terms together:
[tex]\[
-12x^3 + 28x^2
\][/tex]

This simplified expression matches option A:

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

Hence, the correct answer is choice A.