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Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we can distribute [tex]\(-4x^2\)[/tex] across the expression inside the parentheses.
Here's a step-by-step solution:
1. Distribute [tex]\(-4x^2\)[/tex]:
Multiply [tex]\(-4x^2\)[/tex] with each term inside the parentheses [tex]\((3x - 7)\)[/tex]:
- [tex]\(-4x^2 \times 3x = -12x^3\)[/tex]
- [tex]\(-4x^2 \times (-7) = +28x^2\)[/tex]
2. Combine the results:
By combining these results, the expression becomes:
[tex]\(-12x^3 + 28x^2\)[/tex]
Now, let’s match this with the given options:
- A. [tex]\(-12x^3 + 28x^2\)[/tex]
- B. [tex]\(-12x^3 - 28\)[/tex]
- C. [tex]\(-12x^3 - 28x^2\)[/tex]
- D. [tex]\(-12x^3 + 28\)[/tex]
The correct simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which matches option A.
So, the correct answer is A. [tex]\(-12x^3 + 28x^2\)[/tex].
Here's a step-by-step solution:
1. Distribute [tex]\(-4x^2\)[/tex]:
Multiply [tex]\(-4x^2\)[/tex] with each term inside the parentheses [tex]\((3x - 7)\)[/tex]:
- [tex]\(-4x^2 \times 3x = -12x^3\)[/tex]
- [tex]\(-4x^2 \times (-7) = +28x^2\)[/tex]
2. Combine the results:
By combining these results, the expression becomes:
[tex]\(-12x^3 + 28x^2\)[/tex]
Now, let’s match this with the given options:
- A. [tex]\(-12x^3 + 28x^2\)[/tex]
- B. [tex]\(-12x^3 - 28\)[/tex]
- C. [tex]\(-12x^3 - 28x^2\)[/tex]
- D. [tex]\(-12x^3 + 28\)[/tex]
The correct simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which matches option A.
So, the correct answer is A. [tex]\(-12x^3 + 28x^2\)[/tex].
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