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 :

To simplify the expression
[tex]$$-4x^2(3x-7),$$[/tex]
follow these steps:

1. Distribute [tex]$-4x^2$[/tex]:
Multiply [tex]$-4x^2$[/tex] by each term inside the parentheses:
[tex]$$-4x^2 \cdot 3x = -12x^3,$$[/tex]
[tex]$$-4x^2 \cdot (-7) = 28x^2.$$[/tex]

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

3. Identify the correct option:
The simplified expression is
[tex]$$-12x^3 + 28x^2,$$[/tex]
which corresponds to option D.

Thus, the answer is option D.

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