Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property. This property allows us to multiply each term inside the parentheses by the term outside the parentheses.
Here are the steps:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -4 \cdot 3 \cdot x^2 \cdot x = -12x^3
\][/tex]
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = -4 \cdot (-7) \cdot x^2 = 28x^2
\][/tex]
3. Combine the results from steps 1 and 2:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is:
A. [tex]\(-12x^3 + 28x^2\)[/tex]
Here are the steps:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -4 \cdot 3 \cdot x^2 \cdot x = -12x^3
\][/tex]
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = -4 \cdot (-7) \cdot x^2 = 28x^2
\][/tex]
3. Combine the results from steps 1 and 2:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is:
A. [tex]\(-12x^3 + 28x^2\)[/tex]
