DURING LANDING, WITH THE STUDENT PILOT AT THE CONTROLS, THE AIRCRAFT BOUNCED TWICE AND BEGAN TO VEER LEFT. THE CFI ATTEMPTED TO REGAIN DIRECTIONAL CONTROL, BUT WAS NOT SUCCESSFUL. THE AIRPLANE'S RIGHT MAIN LANDING GEAR SEPARATED AS THE AIRPLANE SKIDDED OFF THE LEFT SIDE OF THE RUNWAY. EXAMINATION OF THE FRACTURED AREA OF THE MAIN LANDING GEAR REVEALED THAT IT FAILED DUE TO OVERSTRESS. EXAMINATION OF THE WHEELS REVEALED THAT THEY WERE TOED IN EXCESSIVELY, AND THE TIRE TREADS WERE SEVERELY WORN.