Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], you need to distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses. Let's go through this step-by-step:
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^{2+1} = -12x^3
\][/tex]
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^{2+0} = 28x^2
\][/tex]
3. Combine the results:
The two terms resulting from the distribution are [tex]\(-12x^3\)[/tex] and [tex]\(28x^2\)[/tex]. Putting these together, we get:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option A.
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^{2+1} = -12x^3
\][/tex]
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^{2+0} = 28x^2
\][/tex]
3. Combine the results:
The two terms resulting from the distribution are [tex]\(-12x^3\)[/tex] and [tex]\(28x^2\)[/tex]. Putting these together, we get:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option A.
