因式分解的题目，高分求救，只限今晚!!!

1.(x+1)(x的平方-x+1)-y的三次方-1
2.x^6乘以(x-y)^2n+1+y^6(y-x)^2n+1
3.(x^2+y^2)(x^2-xy+y^2)-2x^2y^2

问题在今晚的10:30关闭，因为怕没有人答，浪费分数，所以悬赏分不高，但是答出来了追加30分，一题10分!!

(60分虽然不多，但希望大家帮帮忙拉，要有解答过程!!)
第二题有点问题吧。x^6-y^6=(x^3+y^3)(x^3-y^3) ???

1题
(x+1)(x^2-x+1)-y^3-1
=x^3+1-y^3-1
=x^3-y^3
=(x-y)(x^2+xy+y^2)

2题
x^6(x-y)^(2n+1)+y^6(y-x)^(2n+1)
=(x-y)^(2n+1)(x^6-y^6)
=(x-y)^(2n+1)(x^3+y^3)(x^3-y^3)
=(x-y)^(2n+1)(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
=(x-y)^(2n+2)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)

3题
(x^2+y^2)(x^2-xy+y^2)-2x^2y^2
=(x^2+y^2)(x+y)(x^2-xy+y^2)/(x+y)-2x^2y^2
=(x^2+y^2)(x^3+y^3)/(x+y)-(2x^3y^2+2x^2y^3)/(x+y)
通分=(x^5+y^5-x^2y^3-x^3y^2)/(x+y)
=(x^2-y^2)(x^3-y^3)/(x+y)
=(x-y)(x^3-y^3)
=(x-y)^2(x^2+xy+y^2)

没问题，把6次方看成3次方再平方
[(x^3)^2-(y^3)^2]把小括号的看成整体，用平方差公式

1.(x+1)(x^2-x+1)-y^3-1
=x^3+1-y^3-1
=(x-y)(x^2-xy+y^2)
2.x^6(x-y)^2n+1+y^6(y-x)^2n+1
=(x-y)^(2n+1)(x^6-y^6)
=(x-y)^(2n+1)(x^3+y^3)(x^3-y^3)
=(x-y)^(2n+1)(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
=(x-y)^(2n+2)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)
3.(x^2+y^2)(x^2-xy+y^2)-2x^2y^2
=x^4-x^3y+x^2y^2+y^2x^2-xy^3+y^4-2x^2y^2