Answer :
Let's simplify the expression [tex]\( -4x^2(3x - 7) \)[/tex] step-by-step.
1. Distribute [tex]\( -4x^2 \)[/tex] across the terms in the parentheses:
[tex]\[
-4x^2(3x - 7)
\][/tex]
2. Multiply [tex]\( -4x^2 \)[/tex] by each term inside the parentheses:
- First, multiply [tex]\( -4x^2 \)[/tex] by [tex]\( 3x \)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
- Next, multiply [tex]\( -4x^2 \)[/tex] by [tex]\( -7 \)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
3. Combine the terms to form the simplified expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\( -12x^3 + 28x^2 \)[/tex].
The correct answer is:
D. [tex]\( -12x^3 + 28 x^2 \)[/tex]
1. Distribute [tex]\( -4x^2 \)[/tex] across the terms in the parentheses:
[tex]\[
-4x^2(3x - 7)
\][/tex]
2. Multiply [tex]\( -4x^2 \)[/tex] by each term inside the parentheses:
- First, multiply [tex]\( -4x^2 \)[/tex] by [tex]\( 3x \)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
- Next, multiply [tex]\( -4x^2 \)[/tex] by [tex]\( -7 \)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
3. Combine the terms to form the simplified expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\( -12x^3 + 28x^2 \)[/tex].
The correct answer is:
D. [tex]\( -12x^3 + 28 x^2 \)[/tex]
