extension / extra time
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extension
The postponement of an end date or deadline, for example for a contract, subscription, or permit.
Ich habe eine Verlängerung meines Arbeitsvertrags um ein weiteres Jahr erhalten.
I received a one-year extension of my employment contract.
'Verlängerung' (extension) is a noun derived from the verb 'verlängern' (to extend / to make longer). The verb itself means 'to make longer' (lang → länger → verlängern: long → longer → extend). So the 'Verlängerung' (extension) is the result or process of making something longer.
Können Sie bitte mein Hotelzimmer um eine Nacht verlängern?
Could you please extend my hotel room by one night?
In bureaucratic or business contexts, 'Verlängerung' (extension) is often used with nouns like 'Vertrag' (contract), 'Visum' (visa), 'Frist' (deadline), or 'Abonnement' (subscription). You can 'eine Verlängerung beantragen' (apply for an extension), 'bekommen' (get one), or 'genehmigen' (approve one).
Ich muss dringend die Verlängerung für mein Visum beantragen.
I urgently need to apply for an extension for my visa.
In sports contexts, there is the fixed expression 'in die Verlängerung gehen' (to go into extra time). It means that the additional playing time begins because the score is tied.
Das Spiel war so spannend, dass es in die Verlängerung gehen musste.
The game was so exciting that it had to go into extra time.
This meaning refers to a physical additional part. Typical examples are a 'Tischverlängerung' (table extension) or a 'Verlängerungskabel' (extension cord) for electricity.
Hast du ein Verlängerungskabel? Die Steckdose ist zu weit weg.
Do you have an extension cord? The outlet is too far away.
expansion / extension
'die Erweiterung' and 'die Verlängerung' both mean that something becomes bigger or gets more of something. The difference lies in the direction or type of change. 'Erweiterung' is used when the scope, content, or area becomes larger, for example a building, a course, or software. 'Verlängerung' is used when something lasts longer, becomes longer, or a deadline ends later. In sports, 'Verlängerung' also means extra time. The words can be confused because both are a kind of increase. Practically speaking: more content or more area is an Erweiterung; more time or more length is a Verlängerung.
Wegen der vielen Anfragen erlaubt die Bibliothek eine Verlängerung der Leihfrist.
Because of the many requests, the library is allowing an extension of the loan period.
Die Erweiterung des Kurses bringt neue Themen und mehr Übungen.
The expansion of the course brings new topics and more exercises.