College

Select the correct answer.

Simplify the expression [tex]-4x^2(3x-7)[/tex]

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

Answer :

Sure, let's simplify the expression step-by-step:

We have the expression:
[tex]\[ -4x^2(3x - 7) \][/tex]

To simplify this, we will distribute [tex]\( -4x^2 \)[/tex] to each term inside the parentheses.

1. Distribute [tex]\( -4x^2 \)[/tex] to [tex]\( 3x \)[/tex]:
[tex]\[ -4x^2 \times 3x = -12x^3 \][/tex]

2. Distribute [tex]\( -4x^2 \)[/tex] to [tex]\( -7 \)[/tex]:
[tex]\[ -4x^2 \times -7 = 28x^2 \][/tex]

Now we combine these results:
[tex]\[ -12x^3 + 28x^2 \][/tex]

Thus, the simplified expression is:
[tex]\[ -12x^3 + 28x^2 \][/tex]

Looking at the options given, the correct answer is:
[tex]\[ D. -12x^3 + 28x^2 \][/tex]