Question

下列各式分解因式正确的是

1. A.
   (x-y)²-(x-y)＝(x-y)(x-y)²
2. B.
   (x-y)²-(x-y)＝(x-y)(x-y)＝(x-y)²
3. C.
   (x-y)²-(y-x)＝(x-y)²-(x-y)＝(x-y)(x-y-1)
4. D.
   (x-y)²-(y-x)＝(x-y)²+(x-y)＝(x-y)(x-y+1)

Answer 1

D
A式(x-y)²-(x-y)＝(x-y)(x-y-1)≠(x-y)(x-y)²．故A是错误的；B式中第二项提出公因式x-y后漏掉了“1”；C式中x-y与y-x只差一个符号，分解时没变换符号，应为(x-y)²-(y-x)＝(x-y)²+(x-y)＝(x-y)(x-y+1)．故选D．