x^5n+x^n+1
=x^5n+x^4n+x^3n-x^4n-x^3n-x^2n+x^2n+x^n+1
=x^3n(x^2n+x^n+1)-x^2n(x^2n+x^n+1)+(x^2n+x^n+1)
=(x^2n+x^n+1)(x^3n-x^2n+1)
2a^2-a^2b+(b-2)(ab-a)^2
=(b-2)(ab-a)^2-a^2b+2a^2
=(b-2)(ab-a)^2-a^2(b-2)
=(b-2)[(ab-a)^2-a^2]
=(b-2)(ab-a+a)(ab-a-a)
=(b-2)(ab)(ab-2a)
=a(b-2)(ab)(b-2)
=ba^2*(b-2)^2
x5+x4+x3+x2+x+1
=(x5+x4)+(x3+x2)+(x+1)
=x^4(x+1)+x^2(x+1)+(x+1)
=(x+1)(x^4+x^2+1)
x^4+y^4-2x^2y^2-2x^2-2y^2+1
=x^4-2x^2y^2+y^4-2x^2-2y^2+1
=(x^2-y^2)^2-2(x^2-y^2)+1
=(x^2-y^2-1)^2