Question

Add the expressions.

Expression 1: −3k+4k3−2
−
3
𝑘
+
4
𝑘
3
−
2


Expression 2: 9k2−3k3+4k−3
9
𝑘
2
−
3
𝑘
3
+
4
𝑘
−
3


(2 points)
k3+
𝑘
3
+
k2+
𝑘
2
+
k+
𝑘
+

Answer 1

To add the two expressions, we'll combine like terms from both the expressions:

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

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

Now, let's reorganize each expression by grouping like terms:

From Expression 1:
- \(4k^3\) (cubic term),
- \(-3k\) (linear term),
- \(-2\) (constant).

From Expression 2:
- \(-3k^3\) (cubic term),
- \(9k^2\) (quadratic term),
- \(4k\) (linear term),
- \(-3\) (constant).

Now let's combine the like terms:

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

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

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

4. Combine the constant terms:
\[
-2 - 3 = -5
\]

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

So the final result after adding the two expressions is:
\[
k^3 + 9k^2 + k - 5
\]