To add the given expressions, we first align the terms based on their degree:
### Expression 1:
\(-3k + 4k^3 - 2\)
### Expression 2:
\(9k^2 - 3k^3 + 4k - 3\)
Now, let's identify their terms:
- **Cubic terms**: \(4k^3\) from Expression 1 and \(-3k^3\) from Expression 2.
- **Quadratic terms**: \(9k^2\) from Expression 2 (no quadratic term in Expression 1).
- **Linear terms**: \(-3k\) from Expression 1 and \(4k\) from Expression 2.
- **Constant terms**: \(-2\) from Expression 1 and \(-3\) from Expression 2.
Now, we can add the matching terms:
1. **Cubic terms**:
\(4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3\)
2. **Quadratic terms**:
\(0 + 9k^2 = 9k^2\)
3. **Linear terms**:
\(-3k + 4k = (4 - 3)k = 1k = k\)
4. **Constant terms**:
\(-2 - 3 = -5\)
### Final combined expression:
Putting all of this together, we get:
\[
k^3 + 9k^2 + k - 5
\]
Thus, the result of adding the two expressions is:
\[
k^3 + 9k^2 + k - 5
\]