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Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], follow these steps:
1. Distribute the [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
This means you multiply [tex]\(-4x^2\)[/tex] by both [tex]\(3x\)[/tex] and [tex]\(-7\)[/tex].
2. Calculate the products:
- 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]
3. Combine the terms to get the simplified expression:
- Combine the results from the multiplication steps:
[tex]\[
-12x^3 + 28x^2
\][/tex]
The simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option C. [tex]\(-12 x^3 + 28 x^2\)[/tex].
1. Distribute the [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
This means you multiply [tex]\(-4x^2\)[/tex] by both [tex]\(3x\)[/tex] and [tex]\(-7\)[/tex].
2. Calculate the products:
- 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]
3. Combine the terms to get the simplified expression:
- Combine the results from the multiplication steps:
[tex]\[
-12x^3 + 28x^2
\][/tex]
The simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option C. [tex]\(-12 x^3 + 28 x^2\)[/tex].
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