Definition: to try to make someone like you and treat you well by behaving in a way you think will please them

Example: Julia knows how to play up to the supervisors - she can always get time off work when she wants it.

https://dictionary.cambridge.org/dictionary/english/play-up-...

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Note added at 1 hr (2019-01-03 03:14:56 GMT)
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Here is a list of related phrases and idioms:

https://www.macmillandictionary.com/thesaurus-category/briti...

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Note added at 1 hr (2019-01-03 03:21:08 GMT)
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I think there are differences between خودشیرینی and چاپلوسی, but if we take them to be near synonyms, you can also say "ingratiate oneself with someone" or "flattery".

https://fa.wikipedia.org/wiki/چاپلوسی

https://en.wikipedia.org/wiki/Flattery

Flattery (also called adulation or blandishment) is the act of giving excessive compliments, generally for the purpose of ingratiating oneself with the subject.

این دو اصطلاح هم برای خود شیرینی کردن به کار می روند:
curry favour (disapproving): to praise someone, especially someone in authority, in a way that is not sincere, in order to get some advantage for yourself
• He's always trying to curry favour with the boss.

brown-nose (informal): to try too hard to please someone, especially someone in a position of authority, in a way that other people find unpleasant
• The rest of the class were sick of watching him brown-nose.

If one person licks another person's boots, they do things or say things to please that person, often because the second person is powerful. Even if you didn't have an official position you'd still be powerful locally and everybody'd be licking your boots. Note: You can call someone who does this a bootlicker. Everyone in Bob's immediate circle was a skilled bootlicker. Note: You use these expressions to show that you find this behaviour unpleasant
یعنی حرفای بزنی و کارایی بکنی که طرف خوشش بیاد چون اون طرف قدرمندتره و میخواید به نفعی برسید. مثلا واسه رئیس

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Ingratiate