Answer:
(x - y) (y + x - 2)
Step-by-step explanation:
Factor the following:
x (x - 2) - y (y - 2)
x (x - 2) = x^2 - 2 x:
x^2 - 2 x - y (y - 2)
-y (y - 2) = 2 y - y^2:
-2 x + x^2 + 2 y - y^2
-2 x + x^2 + 2 y - y^2 = (x - 1)^2 - (y - 1)^2:
(x - 1)^2 - (y - 1)^2
Factor the difference of two squares. (x - 1)^2 - (y - 1)^2 = ((x - 1) - (y - 1)) ((x - 1) + (y - 1)):
(-1 + x - (y - 1)) (-1 + x - 1 + y)
Grouping like terms, -1 + x - 1 + y = y + x + (-1 - 1):
y + x + (-1 - 1) (-1 + x - (y - 1))
-1 - 1 = -2:
(-1 + x - (y - 1)) (y + x + -2)
-(y - 1) = 1 - y:
(-1 + x + 1 - y) (y + x - 2)
Grouping like terms, -1 + x + 1 - y = -y + x + (1 - 1):
-y + x + (1 - 1) (y + x - 2)
1 - 1 = 0:
Answer: (x - y) (y + x - 2)
