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Answer :
To simplify the expression [tex]\(-4 x^2 (3 x - 7)\)[/tex], let's go through it step by step through the process of distribution:
1. Distribute the [tex]\(-4 x^2\)[/tex] across the terms inside the parentheses:
[tex]\[
-4 x^2 \cdot (3 x - 7)
\][/tex]
2. Apply the distributive property:
[tex]\[
-4 x^2 \cdot 3 x + (-4 x^2) \cdot (-7)
\][/tex]
3. Multiply each term separately:
- For the first term:
[tex]\[
-4 x^2 \cdot 3 x = -12 x^3
\][/tex]
- For the second term:
[tex]\[
-4 x^2 \cdot (-7) = 28 x^2
\][/tex]
4. Combine the simplified terms:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Thus, the simplified expression is [tex]\(-12 x^3 + 28 x^2\)[/tex].
Now, we match this with the given options:
A. [tex]\(-12 x^3 + 28 x^2\)[/tex]
B. [tex]\(-12 x^3 - 28\)[/tex]
C. [tex]\(-12 x^3 - 28 x^2\)[/tex]
D. [tex]\(-12 x^3 + 28\)[/tex]
The correct answer is:
A. [tex]\(-12 x^3 + 28 x^2\)[/tex]
1. Distribute the [tex]\(-4 x^2\)[/tex] across the terms inside the parentheses:
[tex]\[
-4 x^2 \cdot (3 x - 7)
\][/tex]
2. Apply the distributive property:
[tex]\[
-4 x^2 \cdot 3 x + (-4 x^2) \cdot (-7)
\][/tex]
3. Multiply each term separately:
- For the first term:
[tex]\[
-4 x^2 \cdot 3 x = -12 x^3
\][/tex]
- For the second term:
[tex]\[
-4 x^2 \cdot (-7) = 28 x^2
\][/tex]
4. Combine the simplified terms:
[tex]\[
-12 x^3 + 28 x^2
\][/tex]
Thus, the simplified expression is [tex]\(-12 x^3 + 28 x^2\)[/tex].
Now, we match this with the given options:
A. [tex]\(-12 x^3 + 28 x^2\)[/tex]
B. [tex]\(-12 x^3 - 28\)[/tex]
C. [tex]\(-12 x^3 - 28 x^2\)[/tex]
D. [tex]\(-12 x^3 + 28\)[/tex]
The correct answer is:
A. [tex]\(-12 x^3 + 28 x^2\)[/tex]
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