Factorize??

x - y - x^2 + 2xy - y^2
= (x - y) - (x^2 - 2xy + y^2)
= (x - y) - (x - y)^2
= (x - y)[1 - (x - y)]
= (x - y)(1 - x + y)

2007-05-31 14:07:40 補充：
x - y - x^2 2xy - y^2= (x - y) - (x^2 - 2xy y^2)

2007-05-31 14:08:02 補充：
x - y - x^2 2xy - y^2= (x - y) - (x^2 - 2xy y^2) ------ 將之分成兩組= (x - y) - (x - y)^2 ------ 後一組用恒等式"a^2 - 2ab b^2 = (a - b)^2"計算= (x - y)[1 - (x - y)] ------ 發現前後兩組有共同因式 common factor, (x - y), 抽其出來= (x - y)(1 - x y)

Factorize x - y - x^2 + 2xy - y^2

(x - y) - (x^2 - 2xy + y^2)
=(x - y) - (x - y)^2
=(x - y) (1 - x + y)

Ans：答案係 (x - y) (1 - x + y)。