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 [tex]\( (3x - 7) \)[/tex].
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
Here, you multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then multiply the variables [tex]\(x^2 \times x\)[/tex] to get [tex]\(x^{2+1} = x^3\)[/tex].
3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and the variable remains as [tex]\(x^2\)[/tex].
4. Combine the results:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified form of the expression [tex]\(-4x^2(3x - 7)\)[/tex] is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
C. [tex]\(-12x^3 + 28x^2\)[/tex]
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses [tex]\( (3x - 7) \)[/tex].
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
Here, you multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then multiply the variables [tex]\(x^2 \times x\)[/tex] to get [tex]\(x^{2+1} = x^3\)[/tex].
3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and the variable remains as [tex]\(x^2\)[/tex].
4. Combine the results:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified form of the expression [tex]\(-4x^2(3x - 7)\)[/tex] is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
C. [tex]\(-12x^3 + 28x^2\)[/tex]
