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

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

Answer :

To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property. This property allows us to multiply each term inside the parentheses by the factor outside the parentheses.

Here's how you can do it step-by-step:

1. Multiply [tex]\(-4x^2\)[/tex] by the first term inside the parentheses, [tex]\(3x\)[/tex]:

[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]

2. Multiply [tex]\(-4x^2\)[/tex] by the second term inside the parentheses, [tex]\(-7\)[/tex]:

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

3. Combine the results from the two multiplications:

[tex]\[
-12x^3 + 28x^2
\][/tex]

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

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

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