Decompose $V(Y^4-X^2,Y^4-X^2Y^2+XY^2-X^3)\subset A^2(C)$ into irreducible components.
I tried like this:
$Y^4-X^2=(Y^2-X)(Y^2+X)$ and $Y^4-X^2Y^2+XY^2-X^3=(Y+X)(Y-X)(Y^2+X)$. What should I do from here?? Should I take the common factor of both these terms??