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Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], let's use the distributive property. This means we'll multiply each term inside the parentheses by [tex]\(-4x^2\)[/tex].
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{2+1} = -12x^3
\][/tex]
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = +28x^2
\][/tex]
Now, let's combine the results of these two multiplications:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Thus, the simplified expression is:
[tex]\(\boxed{-12x^3 + 28x^2}\)[/tex]
So, the correct answer is option B: [tex]\(-12x^3 + 28x^2\)[/tex].
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{2+1} = -12x^3
\][/tex]
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = +28x^2
\][/tex]
Now, let's combine the results of these two multiplications:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Thus, the simplified expression is:
[tex]\(\boxed{-12x^3 + 28x^2}\)[/tex]
So, the correct answer is option B: [tex]\(-12x^3 + 28x^2\)[/tex].
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