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Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we'll follow these steps:
1. Distribute the [tex]\(-4x^2\)[/tex] across the terms inside the parentheses: This involves multiplying [tex]\(-4x^2\)[/tex] by each term inside the parentheses [tex]\((3x - 7)\)[/tex].
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{3}
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
2. Combine both terms to get the simplified expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
The simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Thus, the correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].
1. Distribute the [tex]\(-4x^2\)[/tex] across the terms inside the parentheses: This involves multiplying [tex]\(-4x^2\)[/tex] by each term inside the parentheses [tex]\((3x - 7)\)[/tex].
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{3}
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
2. Combine both terms to get the simplified expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
The simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Thus, the correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].
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