Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], follow these steps:
1. Distribute [tex]\(-4x^2\)[/tex]: Apply the distributive property by multiplying [tex]\(-4x^2\)[/tex] with each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by [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] to get [tex]\(x^{3}\)[/tex]).
- Next, multiply [tex]\(-4x^2\)[/tex] by [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 the [tex]\(x^2\)[/tex] remains the same since there is no [tex]\(x\)[/tex] in [tex]\(-7\)[/tex]).
2. Combine the results: Now, combine the terms obtained from the distribution:
[tex]\[
-12x^{3} + 28x^{2}
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is A. [tex]\(-12x^3 + 28x^2\)[/tex].
1. Distribute [tex]\(-4x^2\)[/tex]: Apply the distributive property by multiplying [tex]\(-4x^2\)[/tex] with each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by [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] to get [tex]\(x^{3}\)[/tex]).
- Next, multiply [tex]\(-4x^2\)[/tex] by [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 the [tex]\(x^2\)[/tex] remains the same since there is no [tex]\(x\)[/tex] in [tex]\(-7\)[/tex]).
2. Combine the results: Now, combine the terms obtained from the distribution:
[tex]\[
-12x^{3} + 28x^{2}
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is A. [tex]\(-12x^3 + 28x^2\)[/tex].
