Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we will use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].
Here's how you can simplify it step-by-step:
1. Distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses:
[tex]\(-4x^2 \times 3x\)[/tex] and [tex]\(-4x^2 \times (-7)\)[/tex].
2. Multiply each term individually:
- For the first term, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{2+1} = -12x^3
\][/tex]
- For the second term, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = +28x^2
\][/tex]
3. Combine the results:
Combine both terms to get the simplified expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Now, let's match this with the provided options:
A. [tex]\(-12 x^3+28\)[/tex]
B. [tex]\(-12 x^3-28 x^2\)[/tex]
C. [tex]\(-12 x^3+203 x^2\)[/tex]
D. [tex]\(-12 x^3-28\)[/tex]
The correct answer is not listed among the provided options. Please double-check the options or the initial problem to ensure accuracy.
Here's how you can simplify it step-by-step:
1. Distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses:
[tex]\(-4x^2 \times 3x\)[/tex] and [tex]\(-4x^2 \times (-7)\)[/tex].
2. Multiply each term individually:
- For the first term, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{2+1} = -12x^3
\][/tex]
- For the second term, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = +28x^2
\][/tex]
3. Combine the results:
Combine both terms to get the simplified expression:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Now, let's match this with the provided options:
A. [tex]\(-12 x^3+28\)[/tex]
B. [tex]\(-12 x^3-28 x^2\)[/tex]
C. [tex]\(-12 x^3+203 x^2\)[/tex]
D. [tex]\(-12 x^3-28\)[/tex]
The correct answer is not listed among the provided options. Please double-check the options or the initial problem to ensure accuracy.
