## Simplifying Algebraic Expressions

This article will guide you through simplifying the algebraic expression: **(9a³b + 6ab - 4) - (10a³b - 6a²b² - 6)**. We'll break down each step to make it easy to follow.

### Step 1: Distributing the Negative Sign

The first step is to distribute the negative sign outside the second set of parentheses. Remember that multiplying a negative sign by a positive term results in a negative term, and multiplying a negative sign by a negative term results in a positive term.

**(9a³b + 6ab - 4) - (10a³b - 6a²b² - 6)**
becomes
**(9a³b + 6ab - 4) - 10a³b + 6a²b² + 6**

### Step 2: Combining Like Terms

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

**(9a³b - 10a³b) + 6ab + 6a²b² + (-4 + 6)**

### Step 3: Simplifying the Expression

Finally, perform the arithmetic operations on the coefficients of each term:

**-a³b + 6ab + 6a²b² + 2**

### The Simplified Expression

The simplified form of the expression **(9a³b + 6ab - 4) - (10a³b - 6a²b² - 6)** is **-a³b + 6ab + 6a²b² + 2**.

This process illustrates the fundamental principles of simplifying algebraic expressions, involving distributing negative signs and combining like terms. By applying these steps consistently, you can effectively simplify complex expressions and arrive at their simplified forms.