To add the two expressions, we need to combine like terms. Here are the expressions:
Expression 1: \(-3k + 4k^3 - 2\)
Expression 2: \(9k^2 - 3k^3 + 4k - 3\)
Now, we can write out both expressions together and align like terms:
\[ (-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3) \]
Now we will combine like terms:
- Cubic terms: \(4k^3 - 3k^3 = 1k^3\)
- Quadratic terms: \(9k^2\) (only one term)
- Linear terms: \(-3k + 4k = 1k\)
- Constant terms: \(-2 - 3 = -5\)
Putting it all together, we have:
\[ k^3 + 9k^2 + k - 5 \]
Thus, the result of adding the two expressions is:
\[ \boxed{k^3 + 9k^2 + k - 5} \]