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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 :

Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step by step.

1. Distribute the [tex]\(-4x^2\)[/tex] across the terms inside the parentheses [tex]\(3x - 7\)[/tex]:

- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]

- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = +28x^2
\][/tex]

2. Combine both results:

Put these terms together:
[tex]\[
-12x^3 + 28x^2
\][/tex]

So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].

Therefore, the correct answer is:
B. [tex]\(-12x^3 + 28x^2\)[/tex]

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