to open the window

[blouen]

Would you mind to open the window?
Would you mind opening the window?

* Which one's good?

[buggles]

Always and only, the second one.

Buggles(not a teacher)

[rj1948]

Would you mind opening the window? -correct
It is a polite request.

[mykwyner]

The first sentence is correct with an action verb in the place of mind.

Would you like to open the window?
Would you try to open the window?
Would you remember to open the window?

[Neillythere]

Hi, as a Brit and mentor, but not a teacher:

"Would you mind opening the window?" would translate as:
"Would you mind opening the window for me"
i.e. I would like the window opened. Would you do it for me. I can't reach it.

Whereas: "Would you like to open the window?" would translate as:
"Would you like to open the window for your reasons?"

Or, to put it another way:
"Would you mind breathing my 2nd-hand smoke?" vs
"Would you like to breathe my 2nd-hand smoke?"

Not sure. It may just be one of those UKE/AME situations.

Best regards
NT