(x-y)x^6+(y-x)y^6因式分解

(x-y)x^6+(y-x)y^6

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

(x-y)x^6+(y-x)y^6

=(x-y)(x^6-y^6)
=(x-y)(x³+y³)(x³-y³)

(x-y)x^6+(y-x)y^6
=(x-y)x^6-(x-y)y^6
=(x-y)(x^6-y^6)
=(x-y)(x³+y³)(x³-y³)
=(x-y)(x+y)(x²-xy+y²)(x-y)(x²+xy+y²)
=(x-y)²(x+y)(x²-xy+y²)(x²+xy+y²)

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解: (x-y)x^6+(y-x)y^6
=(x-y)x^6-(x-y)y^6
=(x-y)(x^6-y^6)
=(x-y)(x³+y³)(x³-y³)
=(x-y)(x+y)(x²-xy+y²)(x-y)(x²+xy+y²)
=(x-y)²(x+y)(x²-xy+y²)(x²+xy+y²)

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原式=(x-y)(x^6-y^6)
=(x-y)(x^3+y^3)(x^3-y^3)
=(x+y)(x-y)^2(x^2+xy+y^2)(x^2-xy+y^2)