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