x^6(x^2-y^2)+y^6(y^2-x^2)分解因式

您好：

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

=(x^6-y^6)(x^2-y^2)

=(x^2-y^2)(x^4+x^2y^2+y^4)(x^2-y^2)
=(x^2-y^2)^2(x^4+2x^y^2+y^4-x^2y^2)
=(x+y)²（x-y）²【（x²+y²）²-x²y²】
=(x+y)²(x-y)²(x²+y²+xy)(x²+y²-xy)
=(x+y)²(x-y)²(x²+y²+xy)(x²+y²-xy)

8(x+y)^3+1

=(2x+2y+1)[4(x+y)²-2（x+y）+1]
=(2x+2y+1)(4x²+8xy+y²-2x-2y+1)

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x^6(x^2-y^2)+y^6(y^2-x^2)

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

8(x+y)^3+1

=[2(x+y)]^3+1
=

（x+y）（x-y）（x^3+y^3）（x^3-y^3）