Answer :
To simplify the expression [tex]\(-4 x^2(3 x-7)\)[/tex], let's follow these steps:
1. Distribute the [tex]\(-4 x^2\)[/tex] across the terms inside the parentheses.
The expression inside the parentheses is [tex]\(3x - 7\)[/tex]. We will multiply [tex]\(-4 x^2\)[/tex] by each term inside the parentheses.
2. First, multiply [tex]\(-4 x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4 x^2 \cdot 3x = -12 x^3
\][/tex]
3. Next, multiply [tex]\(-4 x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4 x^2 \cdot -7 = 28 x^2
\][/tex]
4. Combine the results from the multiplications:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Comparing our simplified expression with the choices given, we find that the correct answer is:
B. [tex]\(-12 x^3 - 28 x^2\)[/tex]
1. Distribute the [tex]\(-4 x^2\)[/tex] across the terms inside the parentheses.
The expression inside the parentheses is [tex]\(3x - 7\)[/tex]. We will multiply [tex]\(-4 x^2\)[/tex] by each term inside the parentheses.
2. First, multiply [tex]\(-4 x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4 x^2 \cdot 3x = -12 x^3
\][/tex]
3. Next, multiply [tex]\(-4 x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4 x^2 \cdot -7 = 28 x^2
\][/tex]
4. Combine the results from the multiplications:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Comparing our simplified expression with the choices given, we find that the correct answer is:
B. [tex]\(-12 x^3 - 28 x^2\)[/tex]
