Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we need to distribute [tex]\(-4x^2\)[/tex] to both terms inside the parentheses.
Here's the step-by-step breakdown:
1. Distribute [tex]\(-4x^2\)[/tex] to the first term, [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and add the exponents of [tex]\(x\)[/tex] (2 + 1 = 3) to get [tex]\(x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to the second term, [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and keep the exponent of [tex]\(x\)[/tex] the same as it is (which is 2).
3. Combine the results:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex]. This matches with option B from the given choices:
[tex]\[
B. -12x^3 + 28x^2
\][/tex]
Here's the step-by-step breakdown:
1. Distribute [tex]\(-4x^2\)[/tex] to the first term, [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and add the exponents of [tex]\(x\)[/tex] (2 + 1 = 3) to get [tex]\(x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to the second term, [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and keep the exponent of [tex]\(x\)[/tex] the same as it is (which is 2).
3. Combine the results:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex]. This matches with option B from the given choices:
[tex]\[
B. -12x^3 + 28x^2
\][/tex]
