Question

Разложите на множители x^3-y^3+3y^2-3y+1

Answer 1

$x^3-y^3+3y^2-3y+1=x^3-(y^3-3y^2+3y-1)=x^3-(y-1)^3=\\ \\ =(x-y+1)(x^2+x(y-1)+(y-1)^2)=\boxed{(x-y+1)(x^2-x+xy+y^2-2y+1)}$