## Simplifying Polynomial Expressions

In mathematics, a **polynomial** is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, `5x^6 - 2x^4 + 9x^3 + 2x - 4`

and `7x^5 - 8x^4 + 2x - 11`

are both polynomials.

Let's simplify the expression: `(5x^6 - 2x^4 + 9x^3 + 2x - 4) - (7x^5 - 8x^4 + 2x - 11)`

.

### Step 1: Distribute the Negative Sign

The minus sign in front of the second parenthesis means we need to multiply each term inside the second parenthesis by -1.

This gives us:

`5x^6 - 2x^4 + 9x^3 + 2x - 4 - 7x^5 + 8x^4 - 2x + 11`

### Step 2: Combine Like Terms

Now, we combine the terms with the same variable and exponent.

**x^6 terms:**`5x^6`

**x^5 terms:**`-7x^5`

**x^4 terms:**`-2x^4 + 8x^4 = 6x^4`

**x^3 terms:**`9x^3`

**x terms:**`2x - 2x = 0`

**Constant terms:**`-4 + 11 = 7`

### Step 3: Final Result

Putting all the terms together, we get the simplified expression:

`5x^6 - 7x^5 + 6x^4 + 9x^3 + 7`

This is the simplified form of the original expression.