## Factoring and Simplifying (a + b)(a - b)(b - a)

This expression involves a combination of factors and can be simplified using the properties of algebra. Let's break it down step-by-step.

### Recognizing the Difference of Squares

The first two factors, **(a + b)(a - b)**, represent the difference of squares pattern. This pattern states:
**(x + y)(x - y) = x² - y²**

Applying this pattern to our expression:

(a + b)(a - b) = a² - b²

### Simplifying the Expression

Now we have:

(a² - b²)(b - a)

To simplify further, we can factor out a -1 from the last factor:

(a² - b²)(-1)(a - b)

Notice that the remaining factors now have a common factor (a - b):

(-1)(a - b)(a² - b²)

### Final Result

Finally, we can rearrange the factors and present the simplified expression:

**(a - b)(b² - a²)**

This is the simplified form of the expression (a + b)(a - b)(b - a).