Would you mind my opening the window?
3.Would you mind if I smoke here?
4.Would you mind helping me?ie Would you please help me?
5.Would you mind taking your foot off my hand?
6.Oh,would you mind?I hate to be a bother.
7.Please forgive me,but would you mind repeating your name?
8.It's very close in here.Would you mind opening the window?