Answer :
To simplify the expression [tex]\(\left(x^2 + 7x^3 - 4x\right) - \left(4x^2 - 7x^3 + 2x\right)\)[/tex], we need to subtract the second polynomial from the first.
Here's a step-by-step breakdown:
1. Write down the expression to be simplified:
[tex]\[
(x^2 + 7x^3 - 4x) - (4x^2 - 7x^3 + 2x)
\][/tex]
2. Distribute the negative sign through the second polynomial:
[tex]\[
x^2 + 7x^3 - 4x - 4x^2 + 7x^3 - 2x
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(7x^3 + 7x^3 = 14x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(x^2 - 4x^2 = -3x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-4x - 2x = -6x\)[/tex]
4. Write the simplified expression:
[tex]\[
14x^3 - 3x^2 - 6x
\][/tex]
Therefore, the simplified expression is [tex]\(14x^3 - 3x^2 - 6x\)[/tex].
The correct choice is [tex]\(\text{A) } 14x^3 - 3x^2 - 6x\)[/tex].
Here's a step-by-step breakdown:
1. Write down the expression to be simplified:
[tex]\[
(x^2 + 7x^3 - 4x) - (4x^2 - 7x^3 + 2x)
\][/tex]
2. Distribute the negative sign through the second polynomial:
[tex]\[
x^2 + 7x^3 - 4x - 4x^2 + 7x^3 - 2x
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(7x^3 + 7x^3 = 14x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(x^2 - 4x^2 = -3x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-4x - 2x = -6x\)[/tex]
4. Write the simplified expression:
[tex]\[
14x^3 - 3x^2 - 6x
\][/tex]
Therefore, the simplified expression is [tex]\(14x^3 - 3x^2 - 6x\)[/tex].
The correct choice is [tex]\(\text{A) } 14x^3 - 3x^2 - 6x\)[/tex].
