aufblasen
to inflate
To fill something with air or gas so that it becomes larger and fuller.
Wir müssen noch die Luftmatratze für unseren Gast aufblasen.
We still need to inflate the air mattress for our guest.

to inflate / blow up
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to inflate
To fill something with air or gas so that it becomes larger and fuller.
Wir müssen noch die Luftmatratze für unseren Gast aufblasen.
We still need to inflate the air mattress for our guest.

'Aufblasen' (to inflate, to blow up) is a separable verb. The prefix 'auf' comes at the end in a main clause, but stays attached to the verb in a subordinate clause. In the infinitive with 'zu', 'zu' is placed between 'auf' and 'blasen'.
Er bläst den Reifen mit einer Pumpe auf.
He inflates the tire with a pump.
The verb consists of 'auf' and 'blasen' (to blow). The prefix 'auf-' here reinforces the idea of becoming bigger and increasing in volume. This logic connects the literal meaning (air mattress) with the figurative meanings (problem, ego).
Die Kinder lieben es, Seifenblasen aufzublasen, bis sie platzen.
The children love blowing up soap bubbles until they burst.
The reflexive form 'sich aufblasen' has two meanings: either a person behaves arrogantly, or a body part swells up. The non-reflexive form always refers to making an object bigger, either literally or figuratively.
Er neigt dazu, sich mit seinem Wissen aufzublasen.
He tends to puff himself up with his knowledge.
In the literal meaning, 'aufblasen' (to inflate) is typically used with objects that are filled with air. These include: 'einen Luftballon aufblasen' (to inflate a balloon), 'einen Reifen aufblasen' (to inflate a tire), 'eine Luftmatratze aufblasen' (to inflate an air mattress), or 'ein Schlauchboot aufblasen' (to inflate an inflatable boat).
Kannst du mir helfen, das Schlauchboot für die Kinder aufzublasen?
Can you help me inflate the inflatable boat for the children?
When exaggerating a situation, the structure 'etwas (Akkusativ) zu etwas (Dativ) aufblasen' (to blow something up into something) is often used. This emphasizes the exaggerated result.
Du solltest eine kleine Meinungsverschiedenheit nicht zu einem großen Streit aufblasen.
You shouldn't blow up a small disagreement into a big argument.
to state / boast / report
'angeben' and 'sich aufblasen' can both describe someone coming across as boastful or arrogant. 'angeben' means that someone wants to impress others, for example by talking about possessions, skills, or success. 'sich aufblasen' sounds more figurative and more strongly negative: someone makes themselves seem very important and comes across as exaggeratedly big. Learners may confuse the words because both describe a similar negative behavior. 'angeben' is more neutral in structure and very common in everyday language; 'sich aufblasen' fits when you find the behavior especially exaggerated or ridiculous.

Seit der kleinen Beförderung bläst sie sich im Büro ständig auf.
Since her small promotion, she has constantly been puffing herself up at the office.
Mein Bruder gibt gern damit an, dass er jeden Termin sofort bekommt.
My brother likes to boast that he can get any appointment right away.