Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], you need to distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses. Let's go through this step-by-step:
1. Distribute the first term:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
2. Distribute the second term:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = +28x^2
\][/tex]
3. Combine the terms:
- Put together the results from the distributions:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Thus, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
C. [tex]\(-12x^3 + 28x^2\)[/tex]
1. Distribute the first term:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
2. Distribute the second term:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = +28x^2
\][/tex]
3. Combine the terms:
- Put together the results from the distributions:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Thus, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
C. [tex]\(-12x^3 + 28x^2\)[/tex]
