Making Polite Requests in English

The following phrases are useful expression to make polite request or to ask permission to do something. When we ask someone to do something, or ask if we can do something, it's important to make them the politely. Here are some useful expression that we can say to make polite request and asking permission

Making polite request
"Could you open the window for me, please?"
"Would you mind clsing the door for us, please?"
"Can you close the door for me, please?'

The responses for that polite request can be:
Sure
Certainly
Why not
With a pleasure
I'd be glad to
I am afraid I can't
I am sorry I can't

The pattern:
could and can are followed by the verb without to.
Would you mind is followed by the verb and -ing.

Asking polite permission to do something
"Can I use your phone, please?"
"Could I borrow some money from you, please?"
"Do you mind if I turn on television?"
"Would you mind if I turned off the lamp?"

The responses can be:
No. I don't mind
Not at all
No, of course not
No, that would be fine
I am afraid, yes
Yes, I do mind

The pattern:
Could is more polite that can.
Do you mind if…" is followed by the verb in the present tense.
would you mind if… is followed by the verb in the past tense.