Question

Add the expressions.

Expression 1: −3k+4k3−2


Expression 2: 9k2−3k3+4k−3

Answer 1

To add the two expressions, we will combine like terms from both expressions.

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

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

Now, let's write both expressions together for clarity:

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

Now, we can combine like terms. First, we will rewrite the expressions grouped by their powers of \(k\):

**Grouping by term:**
- \(k^3\) terms: \(4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3\)
- \(k^2\) terms: \(9k^2\)
- \(k\) terms: \(-3k + 4k = (-3 + 4)k = 1k\)
- Constant terms: \(-2 - 3 = -5\)

Putting it all together, we have:
\[
1k^3 + 9k^2 + 1k - 5
\]

This can be written more neatly as:
\[
k^3 + 9k^2 + k - 5
\]

Therefore, the sum of the two expressions is:
\[
\boxed{k^3 + 9k^2 + k - 5}
\]