Question

add the expressions
-3k + 4k to the third power - 2
9k to the second power - 3k to the third power + 4k -3

Answer 1

To add the expressions \(-3k + 4k^3 - 2\) and \(9k^2 - 3k^3 + 4k - 3\), we start by rearranging terms and combining like terms.

First, write both expressions clearly:

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

Now, let's add them together:

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

Combine like terms:

- The \(k^3\) terms: \(4k^3 - 3k^3 = 1k^3\)
- The \(k^2\) terms: \(9k^2\) (there's no other \(k^2\) term)
- The \(k\) terms: \(-3k + 4k = 1k\)
- The constant terms: \(-2 - 3 = -5\)

Now, put it all together:

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

Finally, write the expression in standard form:

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

So, the sum of the expressions is:

\[
\mathbf{k^3 + 9k^2 + k - 5}
\]