Question

Add the expressions.%0D%0A%0D%0AExpression 1: −3k+4k3−2%0D%0A−%0D%0A3%0D%0A𝑘%0D%0A+%0D%0A4%0D%0A𝑘%0D%0A3%0D%0A−%0D%0A2%0D%0A%0D%0AExpression 2: 9k2−3k3+4k−3

Answer 1

Let's combine the two expressions you've provided step by step.

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

First, let's clean it up:
\[
4k^3 + 4k^3 - 3k - 3k - 2 - 2
\]
This simplifies to:
\[
8k^3 - 6k - 4
\]

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

### Combined Expressions
Now, we need to combine Expression 1 (\(8k^3 - 6k - 4\)) and Expression 2 (\(9k^2 - 3k^3 + 4k - 3\)):

\[
(8k^3 - 6k - 4) + (9k^2 - 3k^3 + 4k - 3)
\]

Let's group like terms:

1. **Cubic terms**: \(8k^3 - 3k^3 = 5k^3\)
2. **Quadratic terms**: \(9k^2\) (there's no other quadratic term)
3. **Linear terms**: \(-6k + 4k = -2k\)
4. **Constant terms**: \(-4 - 3 = -7\)

### Final Result
Combining all the above yields:
\[
5k^3 + 9k^2 - 2k - 7
\]

So, the final expression after adding Expression 1 and Expression 2 is:
\[
5k^3 + 9k^2 - 2k - 7
\]