College

Select the correct answer.

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

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

Answer :

To simplify the expression
[tex]$$-4x^2(3x-7),$$[/tex]
we distribute the term [tex]$-4x^2$[/tex] to both terms inside the parentheses.

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

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

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

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

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