Is C[X,Y]/<XY> isomorphic to the product ring (C[X]/<X>)×(C[Y]/<Y>)

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I need help with this. As and are not comaximal ideals I cant direct use the Chinese remainder theorem. Both fails to be integral domain. The right side ring is isomorphic to C×C. But I dont know how to get a difference between this rings. Please help!