多项式因式分解,

题目

多项式因式分解,
(1)y(x-y)+x(x-y) (2)y(x-y)+x(y-x)
(3)a(x-y)^2-b(y-x)^2 (4)a(x-y)^3-b(y-x)^3
(5)a^2b(a-b)-ab^2(a-b)

答案

(1)y(x-y)+x(x-y) 原式＝yx-y^2+x^2-yx=x^2-y^2=(x-y)(x+y) (2)y(x-y)+x(y-x)原式＝yx-y^2+xy-x^2=-(x^2-2xy+y^2)=-(x-y)^2(3)a(x-y)^2-b(y-x)^2 原式＝ (x-y)^2 （a-b） (4)a(x-y)^3-b(y-x)^3原式＝a(x-y)^3+b(x-y)...