a(x^2-y^2)+b(y^2-x^2)
=(a-b)(x^2-y^2)=(a-b)(x-y)(x+y)
-27x^4+18x^3-3x^2=-3X^2(9X^2-6X+1)=-3x^2(3x-1)^2
x^4-1=(x^2-1)(x^2+1)=(x-10(x+1)(x^2+1)
a^4-2a^2b^2+b^4=(a^2-b^2)^2=(a-b)^2(a+b)^2
(a^2-a)^2-(a-1)^2=(a^2-a+a-1)(a^2-a-a+1)
=(a-1)(a+1)(a-1)^2=(a-1)^3(a+1)