Asking for things: who you're talking to (B1 Vocabulary)

You ask for the same thing in different ways, depending on who you're talking to. There's no single 'correct' one — there's the one that fits the person. With a close friend, a direct ask is fine (Can you ...?). With someone you don't know, or for a big favour, choose a softer form (Could you ...? / Would you mind ...?).

Same favour, different people

Would you mind: two shapes

Would you mind comes in two shapes, and who does the action tells you which one to use. When you want the other person to do it, use Would you mind + the -ing form: Would you mind closing the window? — they close it. When you want to do it yourself and you're just asking their OK, use Would you mind if I + the past form: Would you mind if I opened the window? — you open it. Watch the two forms: -ing after mind (closing, not to close), and the past form after if I (opened, not open).