Add the expressions.

Expression 1: -3k + 4k^3 - 2

Expression 2: 9k^2 - 3k^3 + 4k - 3

_k^3 + _k^2 + _k + _

1 answer

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

Expression 1: \(-3k + 4k^3 - 2\)
Expression 2: \(9k^2 - 3k^3 + 4k - 3\)

Now, we can combine like terms:

  1. Cubic Terms:
    From Expression 1: \(4k^3\)
    From Expression 2: \(-3k^3\)
    Combined: \(4k^3 - 3k^3 = 1k^3\)

  2. Quadratic Terms:
    From Expression 1: \(0k^2\) (since it is not present)
    From Expression 2: \(9k^2\)
    Combined: \(0k^2 + 9k^2 = 9k^2\)

  3. Linear Terms:
    From Expression 1: \(-3k\)
    From Expression 2: \(4k\)
    Combined: \(-3k + 4k = 1k\)

  4. Constant Terms:
    From Expression 1: \(-2\)
    From Expression 2: \(-3\)
    Combined: \(-2 - 3 = -5\)

Now, we compile these results:

\[ 1k^3 + 9k^2 + 1k - 5 \]

Thus, the final result is:

\[ k^3 + 9k^2 + k - 5 \]

The filled expression is: 1k^3 + 9k^2 + 1k + (-5)

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