Let's simplify the given expression step by step.

The expression is:

\[
( -9k^3 + 7k^2 + 2k - 1 ) - ( 4k - 5 )
\]

### Step 1: Distribute the negative sign through the second set of parentheses.

\[
-9k^3 + 7k^2 + 2k - 1 - 4k + 5
\]

### Step 2: Combine like terms.

- Combine the \(k^3\) terms: \(-9k^3\) (no like terms, so it stays the same).
- Combine the \(k^2\) terms: \(7k^2\) (no like terms, so it stays the same).
- Combine the \(k\) terms: \(2k - 4k = -2k\).
- Combine the constant terms: \(-1 + 5 = 4\).

### Simplified Expression:

\[
-9k^3 + 7k^2 - 2k + 4
\]

This is the simplified form of the expression.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you factor polynomials like this one?
2. What are the applications of polynomial expressions in real-world problems?
3. How do you solve a polynomial equation set to zero?
4. Can you graph this polynomial function?
5. What are the roots of the polynomial \(-9k^3 + 7k^2 - 2k + 4 = 0\)?

**Tip:** When simplifying expressions, always carefully distribute negative signs and combine like terms to avoid mistakes.

Discover how to simplify the polynomial expression -9k^3 + 7k^2 + 2k - 1 - 4k + 5 through step-by-step guidance. This exercise involves applying the distributive property and combining like terms, making it ideal for students in Grades 9-10.

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