To add the two expressions, we first need to write them together and then combine like terms.
Expression 1:
\(-3k + 4k^3 - 2\)
Expression 2:
\(9k^2 - 3k^3 + 4k - 3\)
Now we can write them together:
\[ (-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3) \]
Now, combine like terms:
- Cubic terms: \(4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3\)
- Quadratic terms: \(9k^2\) (there are no other \(k^2\) terms, so it remains \(9k^2\))
- Linear terms: \(-3k + 4k = (-3 + 4)k = 1k = k\)
- Constant terms: \(-2 - 3 = -5\)
Putting it all together, we have:
\[ k^3 + 9k^2 + k - 5 \]
So, the sum of the two expressions is:
\[ \boxed{k^3 + 9k^2 + k - 5} \]