Answer :
To simplify the expression [tex]\(-4 x^2(3 x - 7)\)[/tex], we'll need to distribute [tex]\(-4 x^2\)[/tex] to each term inside the parentheses. Let's break it down step-by-step:
1. Distribute to the first term:
Multiply [tex]\(-4 x^2\)[/tex] by [tex]\(3 x\)[/tex]:
[tex]\[
-4 x^2 \times 3 x = -12 x^3
\][/tex]
2. Distribute to the second term:
Multiply [tex]\(-4 x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4 x^2 \times (-7) = 28 x^2
\][/tex]
3. Combine the results:
Now, combine the two results from the distribution:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12 x^3 + 28 x^2\)[/tex].
The correct answer is option B. [tex]\(-12 x^3 + 28 x^2\)[/tex].
1. Distribute to the first term:
Multiply [tex]\(-4 x^2\)[/tex] by [tex]\(3 x\)[/tex]:
[tex]\[
-4 x^2 \times 3 x = -12 x^3
\][/tex]
2. Distribute to the second term:
Multiply [tex]\(-4 x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4 x^2 \times (-7) = 28 x^2
\][/tex]
3. Combine the results:
Now, combine the two results from the distribution:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12 x^3 + 28 x^2\)[/tex].
The correct answer is option B. [tex]\(-12 x^3 + 28 x^2\)[/tex].
