Answer :
Let's simplify the expression [tex]\(-4x^2(3x-7)\)[/tex] step-by-step:
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
The expression [tex]\(-4x^2(3x - 7)\)[/tex] indicates that we need to distribute the factor [tex]\(-4x^2\)[/tex] to both terms inside the parentheses, 3x and -7.
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex] and add the exponents of [tex]\(x\)[/tex] (2 from [tex]\(-4x^2\)[/tex] and 1 from [tex]\(3x\)[/tex]) to get [tex]\(x^{3}\)[/tex].
3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. Since both terms have [tex]\(x^2\)[/tex], the result will be [tex]\(28x^2\)[/tex].
4. Combine the two results:
Add the two expressions obtained from the distribution step:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which matches Option A.
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
The expression [tex]\(-4x^2(3x - 7)\)[/tex] indicates that we need to distribute the factor [tex]\(-4x^2\)[/tex] to both terms inside the parentheses, 3x and -7.
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]
Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex] and add the exponents of [tex]\(x\)[/tex] (2 from [tex]\(-4x^2\)[/tex] and 1 from [tex]\(3x\)[/tex]) to get [tex]\(x^{3}\)[/tex].
3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. Since both terms have [tex]\(x^2\)[/tex], the result will be [tex]\(28x^2\)[/tex].
4. Combine the two results:
Add the two expressions obtained from the distribution step:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which matches Option A.
