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

Answer :

To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], follow these steps:

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

2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
Here, we multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex], and then multiply the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x = x^{2+1} = x^3\)[/tex].

3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot -7 = 28x^2
\][/tex]
Here, multiplying the coefficients gives [tex]\(-4 \times -7 = 28\)[/tex], and the [tex]\(x^2\)[/tex] remains as it is.

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

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

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

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