Answer :
Sure, let's simplify the expression step-by-step:
The given expression is [tex]\(-4x^2(3x - 7)\)[/tex].
To simplify this, we will use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].
1. Distributing [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
- Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
2. Combine the results from the distribution step:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the correct answer is:
D. [tex]\(-12x^3 + 28x^2\)[/tex]
The given expression is [tex]\(-4x^2(3x - 7)\)[/tex].
To simplify this, we will use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].
1. Distributing [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
- Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
2. Combine the results from the distribution step:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the correct answer is:
D. [tex]\(-12x^3 + 28x^2\)[/tex]
