因式分解(x^2+xy+y^2)-4xy(x^2+y^2)

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因式分解(x^2+xy+y^2)-4xy(x^2+y^2)
因式分解(x^2+xy+y^2)-4xy(x^2+y^2)

因式分解(x^2+xy+y^2)-4xy(x^2+y^2)
(x^2+xy+y^2)^2-4xy(x^2+y^2)
=[(x^2+2xy+y^2)-xy]^2-4xy[(x^2+y^2+2xy)-2xy]
=[(x+y)^2-xy]^2-4xy[(x+y)^2-2xy]
=(x+y)^4-2xy(x+y)^2+(xy)^2-4xy(x+y)^2+8(xy)^2
=(x+y)^4-6xy(x+y)^2+9(xy)^2
=[(x+y)^2]^2-6xy(x+y)^2+9(xy)^2
=[(x+y)^2-3xy]^2
=(x^2+2xy+y^2-3xy)^2
=(x^2-xy+y^2)^2

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