vertreiben
to drive away
To force someone or something to leave a place; to chase away or banish.
Die laute Musik hat die Vögel aus dem Garten vertrieben.
The loud music drove the birds out of the garden.

to drive away / distribute
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to drive away
To force someone or something to leave a place; to chase away or banish.
Die laute Musik hat die Vögel aus dem Garten vertrieben.
The loud music drove the birds out of the garden.

'Vertreiben' (to drive away / distribute) is an inseparable verb. The prefix 'ver-' remains firmly attached to the verb 'treiben' (to drive) in all sentence forms and tenses and is never placed at the end of the sentence.
Der Bauer vertreibt die Krähen von seinem Feld.
The farmer drives the crows away from his field.
The verb consists of the prefix 'ver-' and the stem 'treiben' (to drive). The prefix gives the verb two main directions: 'wegtreiben' (to drive away) or 'verteilend treiben' (to distribute, sell).
Die Polizei vertrieb die Demonstranten vom Platz.
The police drove the protesters away from the square.
You can recognize the meaning from the object: if the object is a person or an animal, 'vertreiben' usually means 'to chase away'. If the object is a product or goods, it means 'to sell' or 'to distribute'.
Die Regierung vertrieb die feindlichen Spione aus dem Land.
The government drove the enemy spies out of the country.
In the meaning of 'to sell', 'vertreiben' belongs to business and trade language. It describes the entire process of sales and distribution.
Das Unternehmen vertreibt seine Software weltweit.
The company distributes its software worldwide.
The expression 'sich die Zeit vertreiben' (to pass the time) is reflexive. The person passing the time is in the dative. The activity is connected with the preposition 'mit' (with) plus dative.
Ich vertreibe mir die Zeit im Zug mit einem Podcast.
I pass the time on the train with a podcast.
to act / trade
'handeln' and 'vertreiben' can both have to do with goods and business. 'handeln' generally means to buy and sell goods. People often say 'mit etwas handeln' (to trade in something). 'vertreiben' is more specific: a company brings products to market and sells or distributes them to customers or dealers. The words can be confused because both involve selling. 'handeln' is more suitable for business with goods in general. 'vertreiben' is more suitable when it is about the sale of specific products by a company or provider.

Noahs Unternehmen vertreibt neue Software für kleine Arztpraxen.
Noah's company distributes new software for small doctor's offices.
Die Firma handelt seit vielen Jahren mit gebrauchten Maschinen.
The company has been trading in used machines for many years.