To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we will first combine like terms.
Expression 1: \[ -3k + 4k^3 - 2 \]
Expression 2: \[ 9k^2 - 3k^3 + 4k - 3 \]
Now, let's add them together: \[ (-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3) \]
Now we can combine like terms:
-
For \( k^3 \): \[ 4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3 \]
-
For \( k^2 \): \[ 9k^2 = 9k^2 \]
-
For \( k \): \[ -3k + 4k = (-3 + 4)k = 1k = k \]
-
For the constant terms: \[ -2 - 3 = -5 \]
Combining all these, we get: \[ k^3 + 9k^2 + k - 5 \]
So, the final expression in standard form is: \[ k^3 + 9k^2 + k - 5 \]
Thus, the completed expressions are:
- \( k^3 + \)
- \( 9k^2 + \)
- \( k - 5 \)
1 answer