Question

Add the expressions.
Expression 1: -3k + 4k^3 - 2

Expression 2: 9k^2 - 3k^3 + 4k - 3

_k^3 + _k^2 + _k + _

Answer 1

To add the two expressions, we first write them down:

Expression 1: \(-3k + 4k^3 - 2\)
Expression 2: \(9k^2 - 3k^3 + 4k - 3\)

Now, we can combine like terms:

1. **Cubic Terms**:
From Expression 1: \(4k^3\)
From Expression 2: \(-3k^3\)
Combined: \(4k^3 - 3k^3 = 1k^3\)

2. **Quadratic Terms**:
From Expression 1: \(0k^2\) (since it is not present)
From Expression 2: \(9k^2\)
Combined: \(0k^2 + 9k^2 = 9k^2\)

3. **Linear Terms**:
From Expression 1: \(-3k\)
From Expression 2: \(4k\)
Combined: \(-3k + 4k = 1k\)

4. **Constant Terms**:
From Expression 1: \(-2\)
From Expression 2: \(-3\)
Combined: \(-2 - 3 = -5\)

Now, we compile these results:

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

Thus, the final result is:

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

The filled expression is:
1k^3 + 9k^2 + 1k + (-5)