Question

Add the expressions.

Expression 1: -3k + 4k^3 - 2

Expression 2: 9k^2 - 3k^3 + 4k - 3

Answer 1

To add the two expressions, we need to combine like terms. Here are the expressions:

Expression 1: \(-3k + 4k^3 - 2\)

Expression 2: \(9k^2 - 3k^3 + 4k - 3\)

Now, we can write out both expressions together and align like terms:

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

Now we will combine like terms:

1. **Cubic terms**: \(4k^3 - 3k^3 = 1k^3\)
2. **Quadratic terms**: \(9k^2\) (only one term)
3. **Linear terms**: \(-3k + 4k = 1k\)
4. **Constant terms**: \(-2 - 3 = -5\)

Putting it all together, we have:

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

Thus, the result of adding the two expressions is:

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