To add the two expressions, we need to combine like terms from both expressions.
Expression 1:
\(-3k + 4k^3 - 2\)
Expression 2:
\(9k^2 - 3k^3 + 4k - 3\)
Now, we can rewrite the addition of these expressions:
\[ (-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3) \]
Next, we can rearrange and group the like terms (by degree):
\[ (4k^3 - 3k^3) + (9k^2) + (-3k + 4k) + (-2 - 3) \]
Now, we simplify each group:
- For \(k^3\) terms: \(4k^3 - 3k^3 = 1k^3\) or simply \(k^3\)
- For \(k^2\) terms: \(9k^2\) (remains the same)
- For \(k\) terms: \(-3k + 4k = 1k\) or simply \(k\)
- For the constant terms: \(-2 - 3 = -5\)
Now we combine the simplified terms:
\[ k^3 + 9k^2 + k - 5 \]
So, the sum of the two expressions is:
\[ \boxed{k^3 + 9k^2 + k - 5} \]