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I made potatoes au gratin I first boiled the potatoes in the skins then I peeled them some of them are green and I peel that off I cook the potatoes with the sauce and cheese and the potatoes still came out hard I cook them at 350 for approximately 45 minutes today I microwave the potatoes and they were still hard I want to know why my potatoes are still hard after so much cooking

Hard potatoes usually result when the cooking temperature is not high enough to soften the starch in a potato. Usually that combination happens in an older style of slow cooker which does not have a very high temperature setting. As you write that you boiled the potatoes first, we probably need to go back to that first step and check if the potatoes were "done" from the first cooking step. If they were still firm enough to grate, they were likely not fully cooked. Once a sauce was added to them, the uncooked starch in the potatoes may have formed a protective covering over the potatoes, preventing any further moisture to reach their interior and complete the cooking process.  

I did prepare the potatoes ( peeling and slicing) before I made the sauce. So the potatoes formed  the starch coating. Thankle you!  

You are welcome!