## Expanding and Simplifying (x+1)(x-1)

In mathematics, expanding and simplifying expressions is a fundamental skill. Let's look at how to expand and simplify the expression **(x+1)(x-1)**.

### Understanding the Process

Expanding an expression means multiplying out the brackets. We can use the **FOIL** method (First, Outer, Inner, Last) to achieve this:

**First:**Multiply the first terms of each bracket:**x * x = x²****Outer:**Multiply the outer terms of the brackets:**x * -1 = -x****Inner:**Multiply the inner terms of the brackets:**1 * x = x****Last:**Multiply the last terms of each bracket:**1 * -1 = -1**

This gives us: **x² - x + x - 1**

### Simplifying the Expression

Now, we need to combine like terms:

- The terms
**-x**and**x**cancel each other out.

This leaves us with the simplified expression: **x² - 1**

### Conclusion

Therefore, expanding and simplifying the expression **(x+1)(x-1)** results in **x² - 1**. This simplified form is often easier to work with in algebraic manipulations and calculations.