Add the expressions.%0D%0A%0D%0AExpression 1: −3k+4k3−2%0D%0A−%0D%0A3%0D%0A𝑘%0D%0A+%0D%0A4%0D%0A𝑘%0D%0A3%0D%0A−%0D%0A2%0D%0A%0D%0AExpression 2: 9k2−3k3+4k−3

Answer 1

Let's combine the two expressions you've provided step by step.

Expression 1

Given: \[ -3k + 4k^3 - 2 - 3k + 4k^3 - 2 \]

First, let's clean it up: \[ 4k^3 + 4k^3 - 3k - 3k - 2 - 2 \] This simplifies to: \[ 8k^3 - 6k - 4 \]

Expression 2

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

Combined Expressions

Now, we need to combine Expression 1 (\(8k^3 - 6k - 4\)) and Expression 2 (\(9k^2 - 3k^3 + 4k - 3\)):

\[ (8k^3 - 6k - 4) + (9k^2 - 3k^3 + 4k - 3) \]

Let's group like terms:

1. Cubic terms: \(8k^3 - 3k^3 = 5k^3\)
2. Quadratic terms: \(9k^2\) (there's no other quadratic term)
3. Linear terms: \(-6k + 4k = -2k\)
4. Constant terms: \(-4 - 3 = -7\)

Final Result

Combining all the above yields: \[ 5k^3 + 9k^2 - 2k - 7 \]

So, the final expression after adding Expression 1 and Expression 2 is: \[ 5k^3 + 9k^2 - 2k - 7 \]