已知xy=2,x-y=3,求(x+y)(x-y)-y^2+(x-y)^2-(6x^2y-2xy^2)/2y的值.
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已知xy=2,x-y=3,求(x+y)(x-y)-y^2+(x-y)^2-(6x^2y-2xy^2)/2y的值.
![已知xy=2,x-y=3,求(x+y)(x-y)-y^2+(x-y)^2-(6x^2y-2xy^2)/2y的值.](/uploads/image/z/1183347-27-7.jpg?t=%E5%B7%B2%E7%9F%A5xy%3D2%2Cx-y%3D3%2C%E6%B1%82%EF%BC%88x%2By%EF%BC%89%EF%BC%88x-y%EF%BC%89-y%5E2%2B%EF%BC%88x-y%EF%BC%89%5E2-%EF%BC%886x%5E2y-2xy%5E2%29%2F2y%E7%9A%84%E5%80%BC.)
(x+y)(x-y)-y^2+(x-y)^2-(6x^2y-2xy^2)÷2y
=(x+y)(x-y)-y^2+(x-y)^2-2y(3x^2-xy)÷2y
=(x+y)(x-y)-y^2+(x-y)^2-(3x^2-xy)
=(x+y)(x-y)+(x-y)^2-y^2-(3x^2-xy)
=[(x+y)+(x-y)](x-y)-y^2-(3x^2-xy)
=2x(x-y)-y^2-(3x^2-xy)
=2x^2-2xy-y^2-3x^2+xy
=-x^2-xy-y^2
=-(x^2+y^2+xy)
=-(x^2-2xy+y^2+3xy)
=-[(x-y)^2+3xy]
=-[3^2+3*(-2)]
=-(9-6)
=-3
=(x+y)(x-y)-y^2+(x-y)^2-2y(3x^2-xy)÷2y
=(x+y)(x-y)-y^2+(x-y)^2-(3x^2-xy)
=(x+y)(x-y)+(x-y)^2-y^2-(3x^2-xy)
=[(x+y)+(x-y)](x-y)-y^2-(3x^2-xy)
=2x(x-y)-y^2-(3x^2-xy)
=2x^2-2xy-y^2-3x^2+xy
=-x^2-xy-y^2
=-(x^2+y^2+xy)
=-(x^2-2xy+y^2+3xy)
=-[(x-y)^2+3xy]
=-[3^2+3*(-2)]
=-(9-6)
=-3
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