Add the expressions. Expression 1: −3k+4k3−2 Expression 2: 9k2−3k3+4k−3 (2 points)

To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we will combine like terms.

Let's rewrite the expressions clearly:

**Expression 1:**
\[
-3k + 4k^3 - 2
\]

**Expression 2:**
\[
9k^2 - 3k^3 + 4k - 3
\]

Now, combine the two expressions:

\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

Now we can group like terms:

- **Cubic terms ( \(k^3\) ):**
\[
4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3
\]

- **Quadratic terms ( \(k^2\) ):**
\[
9k^2 = 9k^2
\]

- **Linear terms ( \(k\) ):**
\[
-3k + 4k = (-3 + 4)k = 1k = k
\]

- **Constant terms:**
\[
-2 - 3 = -5
\]

Putting it all together, we get:

\[
k^3 + 9k^2 + k - 5
\]

So, the final result of adding the two expressions is:

\[
\boxed{k^3 + 9k^2 + k - 5}
\]