Question

Add the expressions.
Expression 1: -3k + 4k^3 - 2
Expression 2: 9k^2 - 3k^3 + 4k - 3

Answer 1

To add the two expressions, we first write them down and then combine like terms.

Expression 1:
\[
-3k + 4k^3 - 2
\]

Expression 2:
\[
9k^2 - 3k^3 + 4k - 3
\]

Now, let's combine them:

\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

Now, we'll rearrange and group the like terms:
- For \(k^3\) terms: \(4k^3 - 3k^3\)
- For \(k^2\) terms: \(9k^2\)
- For \(k\) terms: \(-3k + 4k\)
- For constant terms: \(-2 - 3\)

Now let's combine them:
1. \(4k^3 - 3k^3 = 1k^3\)
2. \(9k^2\) (remains as is)
3. \(-3k + 4k = 1k\)
4. \(-2 - 3 = -5\)

Putting everything together, we get:
\[
k^3 + 9k^2 + k - 5
\]

Thus, the sum of the two expressions is:
\[
\boxed{k^3 + 9k^2 + k - 5}
\]