Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we'll use the distributive property, which involves multiplying each term inside the parentheses by the term outside.
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]
Here, you multiply [tex]\(-4\)[/tex] by [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and you multiply [tex]\(x^2\)[/tex] by [tex]\(x\)[/tex] to get [tex]\(x^3\)[/tex].
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^{2}
\][/tex]
Here, multiplying [tex]\(-4\)[/tex] by [tex]\(-7\)[/tex] gives [tex]\(28\)[/tex], and [tex]\(x^2\)[/tex] remains as it is.
2. Combine the results of the distribution:
The simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the correct answer is option C: [tex]\(-12x^3 + 28x^2\)[/tex].
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]
Here, you multiply [tex]\(-4\)[/tex] by [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and you multiply [tex]\(x^2\)[/tex] by [tex]\(x\)[/tex] to get [tex]\(x^3\)[/tex].
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^{2}
\][/tex]
Here, multiplying [tex]\(-4\)[/tex] by [tex]\(-7\)[/tex] gives [tex]\(28\)[/tex], and [tex]\(x^2\)[/tex] remains as it is.
2. Combine the results of the distribution:
The simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the correct answer is option C: [tex]\(-12x^3 + 28x^2\)[/tex].
