Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we can distribute [tex]\(-4x^2\)[/tex] across the elements inside the parentheses. Let's break it down step by step:
1. Identify the terms inside the parentheses:
The expression inside the parentheses is [tex]\(3x - 7\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by the first term, [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by the second term, [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
3. Combine the results of the distribution:
The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Thus, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option D.
1. Identify the terms inside the parentheses:
The expression inside the parentheses is [tex]\(3x - 7\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by the first term, [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by the second term, [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
3. Combine the results of the distribution:
The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Thus, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option D.
