To add the two expressions, we'll combine like terms from both the expressions:
Expression 1:
\[
-3k + 4k^3 - 2
\]
Expression 2:
\[
9k^2 - 3k^3 + 4k - 3
\]
Now, let's reorganize each expression by grouping like terms:
From Expression 1:
- \(4k^3\) (cubic term),
- \(-3k\) (linear term),
- \(-2\) (constant).
From Expression 2:
- \(-3k^3\) (cubic term),
- \(9k^2\) (quadratic term),
- \(4k\) (linear term),
- \(-3\) (constant).
Now let's combine the like terms:
1. Combine the \(k^3\) terms:
\[
4k^3 - 3k^3 = 1k^3 = k^3
\]
2. Combine the \(k^2\) terms:
\[
0 + 9k^2 = 9k^2
\]
3. Combine the \(k\) terms:
\[
-3k + 4k = 1k = k
\]
4. Combine the constant terms:
\[
-2 - 3 = -5
\]
Putting it all together, we get:
\[
k^3 + 9k^2 + k - 5
\]
So the final result after adding the two expressions is:
\[
k^3 + 9k^2 + k - 5
\]