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Select the correct answer.

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

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

Answer :

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

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

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

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

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

Among the options provided, this corresponds to option B.

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