To add the two expressions, we'll combine like terms.
Expression 1:
\(-3k + 4k^3 - 2\)
Expression 2:
\(9k^2 - 3k^3\)
Now, let's write them together:
\[ (-3k + 4k^3 - 2) + (9k^2 - 3k^3) \]
Next, we can rearrange the expression by grouping the like terms:
- \(4k^3 - 3k^3\) (cubic terms)
- \(9k^2\) (quadratic term)
- \(-3k\) (linear term)
- \(-2\) (constant term)
Now, let's combine them:
- \(4k^3 - 3k^3 = 1k^3\) or \(k^3\)
- \(9k^2\) remains as is.
- \(-3k\) remains as is.
- \(-2\) remains as is.
Now put it all together:
\[ k^3 + 9k^2 - 3k - 2 \]
So, the result of adding the two expressions is:
\[ k^3 + 9k^2 - 3k - 2 \]