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

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

(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)

=x3-x2y+xy2-y3-(x3+x2y-xy2-y3)=-2x2y+2xy2=-2xy(x-y)

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

=(x平方+y平方)(x-y) -(x-y)(x+y)平方
=(x-y)[(x平方+y平方)-(x+y)平方]
=(x-y)(x平方+y平方-x平方-2xy-y平方)
=-2xy(x-y)