(a-b)(b-a).jpeg "(a+b)(a-b)(b-a)")
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).