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Select the correct answer.

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

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

Answer :

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

1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:

[tex]\(-4x^2 \times 3x\)[/tex] and [tex]\(-4x^2 \times -7\)[/tex].

2. Simplify each term:

- For the first term:

[tex]\(-4x^2 \times 3x = -12x^{2+1} = -12x^3\)[/tex].

- For the second term:

[tex]\(-4x^2 \times -7 = 28x^2\)[/tex].

3. Combine the simplified terms:

The expression becomes [tex]\(-12x^3 + 28x^2\)[/tex].

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

The correct answer is: D. [tex]\(-12x^3 + 28x^2\)[/tex].

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