x^5+x+1和（x+y-2xy)(x+y-2)+(xy-1)^2怎么因式分解

Question

x^5+x+1和（x+y-2xy)(x+y-2)+(xy-1)^2
怎么因式分解

Answer 1

X^5+X+1
＝x^5-x^2+x^2+x+1
=x^2(x^3-1)+(x^2+x+1)
=x^2*(x-1)(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)(x^3-x^2+1)
（x+y-2XY)(x+y-2)+(xy-1)^2
=[（x+y)-2xy][(x+y)-2]+(xy-1)^2
=(x+y)^2-2(xy+1)(x+y)+4xy+x^2y^2-2xy+1
=(x+y)^2-2(xy+1)(x+y)+x^2y^2+2xy+1
=(x+y)^2-2(xy+1)(x+y)+(xy+1)^2
=[(x+y)-(xy+1)]^2
=(x+y-xy-1)^2
=[x(1-y)-(1-y)]^2
=(x-1)^2(1-y)^2
=(x-1)^2(y-1)^2
还有不会的可以找我