Question

Simply the expression.

(4x^3 - 3x^2 + 6x - 4) - (-2x^3 + x^2 - 2)

Answer 1

To simplify the expression \((4x^3 - 3x^2 + 6x - 4) - (-2x^3 + x^2 - 2)\), we first distribute the negative sign across the second polynomial:

\[
(4x^3 - 3x^2 + 6x - 4) + (2x^3 - x^2 + 2)
\]

Next, we combine like terms:

1. Combine the \(x^3\) terms:
\[
4x^3 + 2x^3 = 6x^3
\]

2. Combine the \(x^2\) terms:
\[
-3x^2 - x^2 = -4x^2
\]

3. Combine the \(x\) terms:
\[
6x
\]

4. Combine the constant terms:
\[
-4 + 2 = -2
\]

Putting it all together, we get:

\[
6x^3 - 4x^2 + 6x - 2
\]

Therefore, the simplified expression is:

\[
\boxed{6x^3 - 4x^2 + 6x - 2}
\]