>>7
18=2*3^2
a^2 - b^2 = (a+b)(a-b)
a^3 + b^3 = (a-b)(a^2 -ab+b^2)
を使うと

x^18 - y^18 = (x^9 + y^9) (x^9 - y^9)
= (x^3 + y^3) (x^3 - y^3) (x^6 +(x^3)(y^3)+y^6)(x^6 -(x^3)(y^3)+y^6)
= (x+y)(x-y) (x^2 -xy+y^2)(x^2+xy+y^2)(x^6 +(x^3)(y^3)+y^6)(x^6 -(x^3)(y^3)+y^6)