Question

化简求值：(x+y)(x-y)+(x-y)²-(6x²y-2xy²)÷2y,其中x=-2,y=1/3

(x+y)(x-y)+(x-y)²-(6x²y-2xy²)÷2y,其中x=-2,y=1/3
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Answer 1

(x+y)(x-y)+(x-y)²-(6x²y-2xy²)÷2y
=(x+y)(x-y)+(x-y)²-2xy(3x-y)÷2y
=(x+y)(x-y)+(x-y)²-x(3x-y)
=x^2-y^2+x^2-2xy+y^2-3x^2+xy
=-x^2-xy
=-x(x+y)
=-(-2)(-2+1/3)
= -10/3

Answer 2

(x+y)(x-y)+(x-y)²-(6x²y-2xy²)÷2y
=x²-y²+x²-2xy+y²-2xy(3x-1)÷2y
=2x²-2xy-2x(3x-1)
=2x²-2xy-6x²+2x
=-4x²-2xy+2x
=-2x(2x+y+1)
代入x=-2,y=1/3
原式=-2*(-2)[2*(-2)+(1/3)+1]
=4*[-4+1+(1/3)]
=4*(-8/3)
=-32/3

Answer 3

(x+y)(x-y)+(x-y)^2-(6x^2y-2xy^2)÷2y
=x^2-y^2+x^2-2xy+y^2-3x^2+2xy
=x^2+x^2-3x^2-y^2+y^2-2xy+2xy
=-x^2
x=-2
上式=-4

Answer 4

原式=x^2-y^2+(x^2-2xy+y^2)-3x^2+2xy
=-x^2-xy
=-x(x-y)
=-10/3

Answer 5

=x方-y方+x方-2xy+y方-3x方+xy
=-x方-xy
=-4+2/3
=-10/3