(x2+y2)(x-y)-(x2-y2)(x+y)

问题描述:

(x2+y2)(x-y)-(x2-y2)(x+y)

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