Question

Add the expressions.

Expression 1: −3k+4k3−2


Expression 2: 9k2−3k3+4k−3


(2 points)
k3+
k2+
k+

Answer 1

To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we will first combine like terms.

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

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

Now, let's add them together:
\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

Now we can combine like terms:

- **For \( k^3 \):**
\[
4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3
\]

- **For \( k^2 \):**
\[
9k^2 = 9k^2
\]

- **For \( k \):**
\[
-3k + 4k = (-3 + 4)k = 1k = k
\]

- **For the constant terms:**
\[
-2 - 3 = -5
\]

Combining all these, we get:
\[
k^3 + 9k^2 + k - 5
\]

So, the final expression in standard form is:
\[
k^3 + 9k^2 + k - 5
\]

Thus, the completed expressions are:
- \( k^3 + \)
- \( 9k^2 + \)
- \( k - 5 \)