1 answer
(click or scroll down)
To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we will combine like terms.
Let's rewrite the expressions clearly:
**Expression 1:**
\[
-3k + 4k^3 - 2
\]
**Expression 2:**
\[
9k^2 - 3k^3 + 4k - 3
\]
Now, combine the two expressions:
\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]
Now we can group like terms:
- **Cubic terms ( \(k^3\) ):**
\[
4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3
\]
- **Quadratic terms ( \(k^2\) ):**
\[
9k^2 = 9k^2
\]
- **Linear terms ( \(k\) ):**
\[
-3k + 4k = (-3 + 4)k = 1k = k
\]
- **Constant terms:**
\[
-2 - 3 = -5
\]
Putting it all together, we get:
\[
k^3 + 9k^2 + k - 5
\]
So, the final result of adding the two expressions is:
\[
\boxed{k^3 + 9k^2 + k - 5}
\]