Question

Add the expressions.
Expression 1: $-3k+4k^{3}-2$
Expression 2: $9k^{2}-3k^{3}+4k-3$
(2 points)
$\square $ $k^{3}+\square k^{2}+\square k+\square $

Answer 1

To add the given expressions, we will combine like terms from both expressions.

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

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

### Step 1: Combine the two expressions
\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

### Step 2: Rearrange and combine like terms
Let's write it out:
\[
4k^3 - 3k^3 + 9k^2 + (-3k + 4k) + (-2 - 3)
\]

### Step 3: Combine the coefficients of each like term
1. **For \(k^3\)**:
\[
4k^3 - 3k^3 = 1k^3
\]

2. **For \(k^2\)**:
\[
9k^2 \text{ (only term)}
\]

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

4. **For the constant term**:
\[
-2 - 3 = -5
\]

### Step 4: Write the final result
Putting it all together:
\[
1k^3 + 9k^2 + 1k - 5
\]

### Step 5: Fill in the blanks
Thus, the coefficients are:
- For \(k^3\), the coefficient is **1**.
- For \(k^2\), the coefficient is **9**.
- For \(k\), the coefficient is **1**.
- For the constant, the coefficient is **-5**.

The final expression can be written as:
\[
\boxed{1}k^3 + \boxed{9}k^2 + \boxed{1}k + \boxed{-5}
\]