Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], follow these steps:
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses.
- 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 the results from the distribution.
- You end up with two terms: [tex]\(-12x^3\)[/tex] and [tex]\(28x^2\)[/tex].
3. Write the simplified expression.
- Combine the terms to form the expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
This means the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is [tex]\(-12x^3 + 28x^2\)[/tex], which matches with option D: [tex]\(-12x^3 - 28x^2\)[/tex]. However, upon reviewing, the correct match from the given options would be somewhere else, as option D is listed incorrectly. Hence this needs reevaluation with current option lists.
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses.
- 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 the results from the distribution.
- You end up with two terms: [tex]\(-12x^3\)[/tex] and [tex]\(28x^2\)[/tex].
3. Write the simplified expression.
- Combine the terms to form the expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
This means the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is [tex]\(-12x^3 + 28x^2\)[/tex], which matches with option D: [tex]\(-12x^3 - 28x^2\)[/tex]. However, upon reviewing, the correct match from the given options would be somewhere else, as option D is listed incorrectly. Hence this needs reevaluation with current option lists.
