## Factoring and Simplifying (a+1)(a-1)-2a+2

This expression can be simplified and factored using algebraic techniques. Here's how:

### 1. Expanding the Expression

First, we expand the expression using the difference of squares pattern: (a+1)(a-1) = a² - 1.

Our expression now becomes: **a² - 1 - 2a + 2**

### 2. Combining Like Terms

Next, we combine the constant terms: -1 + 2 = 1

The simplified expression is: **a² - 2a + 1**

### 3. Factoring the Quadratic

The expression is now in the form of a quadratic equation, which can be factored. We look for two numbers that add up to -2 (the coefficient of the middle term) and multiply to 1 (the constant term). These numbers are -1 and -1.

Therefore, the factored form of the expression is: **(a - 1)(a - 1)** or **(a - 1)²**

### Conclusion

The fully simplified and factored form of the expression (a+1)(a-1)-2a+2 is **(a - 1)²**.