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 first need to write them together and then combine like terms.

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

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

Now we can write them together:

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

Now, combine like terms:

1. **Cubic terms:** \(4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3\)
2. **Quadratic terms:** \(9k^2\) (there are no other \(k^2\) terms, so it remains \(9k^2\))
3. **Linear terms:** \(-3k + 4k = (-3 + 4)k = 1k = k\)
4. **Constant terms:** \(-2 - 3 = -5\)

Putting it all together, we have:

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

So, the sum of the two expressions is:

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