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X+y - z = -2a+a-a +b-2b -b +c + c + 2c = -2 a - 2 b + 4 c

x y = [ (c-a) - (a - b) ] [ (c - b) + (a -b) ]

= (c - a)(c -b) + (c - a) (a-b) - (a - b) (c - b) - (a -b)²

= (c - a) (c - b) + (a - b) [c -a - c + b - a + b ]

= (c - a) (c - b) + 2 (a - b) (b - a)

= c² - a c - bc - 2 a² - 2 b² + 5 a b

x + y - z + 2 x y

= -2 a - 2 b + 4 c + 2 c² - 2 a c -2 bc - 4a² - 4b² + 10 ab

= - 2 [a + b - 2 c - 5 a b + a c + b c - c² + a² + b² ]

= -2 [ (a + b - c) - c - 5 ab + c (a + b - c) + a² + b² ]

= - 2 [ (a + b - c) (1 + c) + (a -b)² - (c + 3 ab) ]

x y = [ (c-a) - (a - b) ] [ (c - b) + (a -b) ]

= (c - a)(c -b) + (c - a) (a-b) - (a - b) (c - b) - (a -b)²

= (c - a) (c - b) + (a - b) [c -a - c + b - a + b ]

= (c - a) (c - b) + 2 (a - b) (b - a)

= c² - a c - bc - 2 a² - 2 b² + 5 a b

x + y - z + 2 x y

= -2 a - 2 b + 4 c + 2 c² - 2 a c -2 bc - 4a² - 4b² + 10 ab

= - 2 [a + b - 2 c - 5 a b + a c + b c - c² + a² + b² ]

= -2 [ (a + b - c) - c - 5 ab + c (a + b - c) + a² + b² ]

= - 2 [ (a + b - c) (1 + c) + (a -b)² - (c + 3 ab) ]