Answer :
Sure, let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step-by-step.
1. Distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses. This means you'll multiply [tex]\(-4x^2\)[/tex] by each term inside the parentheses separately.
2. First Term:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
Here, you multiply [tex]\(-4\)[/tex] by [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then combine the powers of [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] to get [tex]\(x^{2+1} = x^3\)[/tex].
3. Second Term:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
Multiply [tex]\(-4\)[/tex] by [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. The [tex]\(x^2\)[/tex] stays as it is since there's no [tex]\(x\)[/tex] to combine with.
4. Combined Expression:
Now, combine the results from both distributions:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option C: [tex]\(-12x^3 + 28x^2\)[/tex].
1. Distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses. This means you'll multiply [tex]\(-4x^2\)[/tex] by each term inside the parentheses separately.
2. First Term:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
Here, you multiply [tex]\(-4\)[/tex] by [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then combine the powers of [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] to get [tex]\(x^{2+1} = x^3\)[/tex].
3. Second Term:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
Multiply [tex]\(-4\)[/tex] by [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. The [tex]\(x^2\)[/tex] stays as it is since there's no [tex]\(x\)[/tex] to combine with.
4. Combined Expression:
Now, combine the results from both distributions:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option C: [tex]\(-12x^3 + 28x^2\)[/tex].
