College

Simplify each expression.

1) [tex]\left(x^2 + 7x^3 - 4x\right) - \left(4x^2 - 7x^3 + 2x\right)[/tex]

A) [tex]14x^3 - 3x^2 - 6x[/tex]
B) [tex]14x^3 - 3x^2 - 2x[/tex]
C) [tex]14x^3 - 6x[/tex]
D) [tex]14x^3 - 2x[/tex]

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].