## Simplifying Polynomial Expressions

In algebra, we often encounter expressions involving variables and constants combined with operations like addition, subtraction, multiplication, and division. These expressions can be simplified by applying the rules of algebra.

One common type of expression is a **polynomial**, which is a combination of terms with different powers of a variable. Let's consider the following polynomial expression:

**(8x³ + 4x² - 6x + 1) - (5x³ + 2x - 9)**

To simplify this expression, we can follow these steps:

### 1. Distribute the Negative Sign

The minus sign in front of the second set of parentheses means we need to multiply each term inside the parentheses by -1:

**(8x³ + 4x² - 6x + 1) + (-5x³ - 2x + 9)**

### 2. Combine Like Terms

Now we can combine the terms that have the same power of x:

**(8x³ - 5x³) + (4x² - 0x²) + (-6x - 2x) + (1 + 9)**

### 3. Simplify

Finally, we can perform the arithmetic operations:

**3x³ + 4x² - 8x + 10**

Therefore, the simplified form of the given polynomial expression is **3x³ + 4x² - 8x + 10**.

**Key Takeaways:**

- Always remember to distribute the negative sign when subtracting polynomials.
- Combine only like terms (terms with the same power of the variable).
- Simplify by performing the arithmetic operations.

By following these steps, you can simplify polynomial expressions and make them easier to work with.