〜ていただけませんか
A highly polite request — "could you possibly … for me?"machine translation
FormationVerb て-form + いただけませんか
〜ていただけませんか is a very polite way of making a request: take いただく (the humble form of もらう), turn it into the potential いただける, and put it in the negative question form — literally, "might I not be able to receive your doing…?". The result is a request far softer than 〜てください.
The politeness ladder for requests, from direct to formal: 〜てください (direct request, learned at N5) → 〜てもらえませんか → 〜ていただけませんか → 〜ていただけないでしょうか. It's precisely the negative-question form that makes it easier for the listener to decline, so the sentence sounds more modest and polite.
Use this pattern with teachers, superiors, and strangers, or when the favor is relatively big; opening with すみませんが makes the sentence even more complete. With close friends, 〜てくれない? or 〜てもらえる? is enough.
Examples
もう一度説明していただけませんか。
Could you possibly explain that one more time?
写真を撮っていただけませんか。
Could you take a photo for me?
すみませんが、もう少しゆっくり話していただけませんか。
Excuse me, could you possibly speak a little more slowly?