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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 :

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

Here are the steps:

1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:

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

2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:

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

3. Combine the results:

The simplified expression is the sum of the two products from steps 1 and 2:

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

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

The correct choice from the given options is:

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

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