College

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 :

To simplify the expression
[tex]$$-4x^2(3x - 7),$$[/tex]
we start by applying the distributive property, which means multiplying the term outside the parentheses by each term inside the parentheses.

1. Multiply [tex]$$-4x^2$$[/tex] by [tex]$$3x$$[/tex]:
[tex]$$
-4x^2 \cdot 3x = -12x^3.
$$[/tex]

2. Multiply [tex]$$-4x^2$$[/tex] by [tex]$$-7$$[/tex]:
[tex]$$
-4x^2 \cdot (-7) = 28x^2.
$$[/tex]

3. Combine the results:
[tex]$$
-12x^3 + 28x^2.
$$[/tex]

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

Comparing with the given options, the correct choice is option D.