Question

因式分解：（x-y）（x^2+xy+y^2)-xy(y-x)

都是对的要我怎么搞最佳答案啊，郁闷

Answer 1

原式=(x-y)(x²+xy+y²)+xy(x-y)
=(x-y)(x²+xy+y²+xy)
=(x-y)(x²+2xy+y²)
=(x-y)(x+y)²

Answer 2

（x-y）（x^2+xy+y^2)-xy(y-x)
＝（x-y）（x^2+xy+y^2)+xy(x-y)
=(x-y)(x²+xy+y²+xy)
=(x-y)(x²+2xy+y²)
=(x-y)(x+y)²

Answer 3

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