Add the expressions. Expression 1: −3k+4k3−2 Expression 2: 9k2−3k3+4k−3 (2 points) k3+ k2+ k+

Answer 1

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

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

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

Now, let's add the two expressions together. We will combine like terms:

1. Combine the \(k^3\) terms:

   • From Expression 1: \(4k^3\)
   • From Expression 2: \(-3k^3\)
   • Combined: \(4k^3 - 3k^3 = 1k^3\) or just \(k^3\)

2. Combine the \(k^2\) terms:

   • Expression 1: There are no \(k^2\) terms.
   • Expression 2: \(9k^2\)
   • Combined: \(0 + 9k^2 = 9k^2\)

3. Combine the \(k\) terms:

   • From Expression 1: \(-3k\)
   • From Expression 2: \(4k\)
   • Combined: \(-3k + 4k = 1k\) or just \(k\)

4. Combine the constant terms:

   • From Expression 1: \(-2\)
   • From Expression 2: \(-3\)
   • Combined: \(-2 - 3 = -5\)

Now, putting everything together, we have: \[ k^3 + 9k^2 + k - 5 \]

Thus, the final result of adding the two expressions is: \[ \boxed{k^3 + 9k^2 + k - 5} \]