Answer: (2x-2y-1)(x-y)
Explanation:
To factor 2(x-y)² - x+y, we first recognize that the expression is a difference of squares, which means it can be factored into the form (a-b)(a+b). To identify the values of a and b, we can look for common factors between the two terms, which are 2(x-y)² and -x+y.
The common factor between 2(x-y)² and -x+y is x-y. We can factor it out by dividing both terms by x-y:
2(x-y)² - x+y = (x-y) * (2(x-y) - 1)
Now we can write the expression as (x-y)(2x-2y-1) .
As you can see (x-y) is common in both the term, so we can factor it out, and we are left with (2x-2y-1)(x-y)