To combine both expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we need to add the coefficients of like terms (i.e., terms with the same power of \( k \)).
Let's write and identify the components of each expression clearly:
Expression 1:
\[ -3k + 4k^3 - 2 \]
- \( k^3 \): \( 4 \)
- \( k^2 \): \( 0 \) (no \( k^2 \) term)
- \( k^1 \): \( -3 \)
- Constant: \( -2 \)
Expression 2:
\[ 9k^2 - 3k^3 + 4k - 3 \]
- \( k^3 \): \( -3 \)
- \( k^2 \): \( 9 \)
- \( k^1 \): \( 4 \)
- Constant: \( -3 \)
Now, we combine like terms:
- For \( k^3 \):
- \( 4 - 3 = 1 \)
- For \( k^2 \):
- \( 0 + 9 = 9 \)
- For \( k^1 \):
- \( -3 + 4 = 1 \)
- For the constant term:
- \( -2 - 3 = -5 \)
Now, we can write the complete expression:
Combining each component, we get: \[ 1k^3 + 9k^2 + 1k - 5 \]
Thus, in the format □k³ + □k² + □k + □, the coefficients are:
- \( \boxed{1} \) for \( k^3 \)
- \( \boxed{9} \) for \( k^2 \)
- \( \boxed{1} \) for \( k \)
- \( \boxed{-5} \) for the constant term
The final expression is: \[ k^3 + 9k^2 + k - 5 \]