Add the expressions.

Question

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: \[ \boxed{1}k^3 + \boxed{9}k^2 + \boxed{1}k + \boxed{-5} \]