Question

Add the expressions:
Expression 1: -3k + 4k^3 - 2
Expression 2: 9k^2 - 3k^3 + 4k - 3

___k^3 + ___k^2 + ___k + ___

the ___ shows the blank and what you need to answer

Answer 1

To add the two expressions, we first align like terms:

1. **Expression 1:** -3k + 4k^3 - 2
2. **Expression 2:** 9k^2 - 3k^3 + 4k - 3

Now, let's combine the terms:

- For \(k^3\):
\[
4k^3 - 3k^3 = 1k^3
\]

- For \(k^2\):
\[
0 + 9k^2 = 9k^2
\]

- For \(k\):
\[
-3k + 4k = 1k
\]

- For the constant:
\[
-2 - 3 = -5
\]

Now, we can write the combined expression as:
\[
1k^3 + 9k^2 + 1k - 5
\]

In terms of the blanks:
- The coefficient of \(k^3\) is **1**.
- The coefficient of \(k^2\) is **9**.
- The coefficient of \(k\) is **1**.
- The constant is **-5**.

So the final answer is:
\[
1k^3 + 9k^2 + 1k - 5
\]

Which fills the blanks:
___k^3 + ___k^2 + ___k + ___ becomes **1** for \(k^3\), **9** for \(k^2\), **1** for \(k\), and **-5** for the constant.