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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 :

To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property. Here are the steps:

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

[tex]\[ -4x^2 \cdot 3x \][/tex]
[tex]\[ -4x^2 \cdot (-7) \][/tex]

Let's handle these one by one.

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

[tex]\[ -4x^2 \cdot 3x = (-4 \cdot 3) \cdot (x^2 \cdot x) = -12x^3 \][/tex]

3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:

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

4. Combine the results:

[tex]\[ -4x^2(3x - 7) = -12x^3 + 28x^2 \][/tex]

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

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

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