Question

Add the expressions.

Expression 1: −3k+4k^3−2


Expression 2: 9k^2−3k^3+4k−3


(2 points)

Answer 1

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

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

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

Now, let's organize the terms by their degree:

1. \(k^3\) terms: \(4k^3\) from Expression 1 and \(-3k^3\) from Expression 2
2. \(k^2\) terms: \(9k^2\) from Expression 2
3. \(k\) terms: \(-3k\) from Expression 1 and \(4k\) from Expression 2
4. Constant terms: \(-2\) from Expression 1 and \(-3\) from Expression 2

Now we will combine the like terms:

1. Combine \(k^3\) terms:
\(4k^3 - 3k^3 = 1k^3\)

2. Combine \(k^2\) terms:
\(0 + 9k^2 = 9k^2\)

3. Combine \(k\) terms:
\(-3k + 4k = 1k\)

4. Combine constant terms:
\(-2 - 3 = -5\)

Putting it all together, we get:

\[
1k^3 + 9k^2 + 1k - 5
\]

This can be written more simply as:

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

So, the sum of the two expressions is:

\(\boxed{k^3 + 9k^2 + k - 5}\)