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 :

To simplify the expression

[tex]$$-4x^2(3x - 7),$$[/tex]

we use the distributive property to multiply [tex]$-4x^2$[/tex] by each term inside the parentheses.

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

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

Now, combine the results:

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

Thus, the simplified expression is

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

This corresponds to option A.

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