## Simplifying Polynomial Expressions: A Step-by-Step Guide

In mathematics, simplifying polynomial expressions often involves combining like terms and arranging them in descending order of their exponents. Let's break down how to simplify the expression: **(7 - 13x^3 - 11x) - (2x^3 + 8 - 4x^5)**.

### 1. Distribute the Negative Sign

First, we need to distribute the negative sign in front of the second set of parentheses. This changes the signs of each term within the parentheses:

(7 - 13x^3 - 11x) + (-2x^3 - 8 + 4x^5)

### 2. Rearrange Terms by Degree

Now, let's rearrange the terms in descending order of their exponents:

4x^5 - 13x^3 - 2x^3 - 11x + 7 - 8

### 3. Combine Like Terms

Finally, combine the terms with the same exponents:

**4x^5 - 15x^3 - 11x - 1**

### Simplified Expression

Therefore, the simplified form of the expression **(7 - 13x^3 - 11x) - (2x^3 + 8 - 4x^5)** is **4x^5 - 15x^3 - 11x - 1**.