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

This article will guide you through the process of simplifying the algebraic expression:

**(7x²y² - 6x³ + xy) - (5x²y² - x³ + xy + x)**

Let's break down the steps involved in simplifying this expression:

### 1. Distributing the Negative Sign

The first step is to distribute the negative sign in front of the second set of parentheses. Remember that multiplying a negative sign by each term inside the parentheses changes the sign of each term:

**(7x²y² - 6x³ + xy) + (-5x²y² + x³ - xy - x)**

### 2. Combining Like Terms

Now, we can combine like terms. Like terms have the same variables raised to the same exponents.

**x²y² terms:**7x²y² - 5x²y² = 2x²y²**x³ terms:**-6x³ + x³ = -5x³**xy terms:**xy - xy = 0**x terms:**-x

### 3. The Simplified Expression

After combining like terms, the simplified expression is:

**2x²y² - 5x³ - x**

Therefore, the simplified form of the expression **(7x²y² - 6x³ + xy) - (5x²y² - x³ + xy + x)** is **2x²y² - 5x³ - x**.