In solving polynomials x cubed plus 8 y cubed?

Answer 1

x3+8y3 = (x+2y)(x2-2xy+4y2)

The discriminant of the quadratic factor is 4y2-16y2 < 0 so there are no real roots.

So the only real root of the original polynomial is x+2y=0 or x = -2y