To add the two expressions, we will first align like terms and then combine them. Here are the two expressions:
Expression 1: \(-3k + 4k^3 - 2\)
Expression 2: \(9k^2 - 3k^3 + 4k - 3\)
Now we'll rewrite them and group the like terms:
\[ \begin{align*} \text{Expression 1:} & \quad -3k + 4k^3 - 2 \ \text{Expression 2:} & \quad -3k^3 + 9k^2 + 4k - 3 \end{align*} \]
Now, we'll combine them:
\[ \begin{align*} (4k^3 - 3k^3) & + (9k^2) + (-3k + 4k) + (-2 - 3) \ = (4 - 3)k^3 & + 9k^2 + (4 - 3)k + (-2 - 3) \ = 1k^3 & + 9k^2 + 1k - 5 \end{align*} \]
Finally, we can write it in standard form:
\[ k^3 + 9k^2 + k - 5 \]
So the sum of the expressions is:
\[ \boxed{k^3 + 9k^2 + k - 5} \]
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