
ausführen
to carry out
To put a plan, an order, a job, or an activity into action; to execute something.
Die Bauarbeiten werden von einer lokalen Firma ausgeführt.
The construction work is being carried out by a local company.
to carry out / to elaborate / to export
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to carry out
To put a plan, an order, a job, or an activity into action; to execute something.
Die Bauarbeiten werden von einer lokalen Firma ausgeführt.
The construction work is being carried out by a local company.

to elaborate
To explain, present, or clarify something in detail.
Könnten Sie Ihre Idee bitte etwas genauer ausführen?
Could you please elaborate on your idea a little more?

to export
To sell and deliver goods or merchandise abroad; to export.
Deutschland führt viele Autos in die ganze Welt aus.
Germany exports many cars all over the world.

to take someone/something out
To go outside with someone (e.g., a partner) or an animal (e.g., a dog), often for a specific purpose such as a walk or a restaurant visit.
Er führt jeden Abend seinen Hund im Park aus.
He takes his dog out in the park every evening.
'Ausführen' (to carry out / to elaborate / to export) is a separable verb. The prefix 'aus' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Architekt führt den Plan exakt aus.
The architect carries out the plan exactly.
The verb consists of the prefix 'aus' and the base verb 'führen' (to lead). The basic idea of bringing something out or leading something to completion connects the different meanings.
Die Firma führt die bestellten Waren morgen aus.
The company will export the ordered goods tomorrow.
In the meaning 'durchführen' (to carry out), the verb is often combined with plans, orders, or work. Typical objects are: an assignment, a plan, a repair, or an instruction.
Der Handwerker hat die Reparatur schnell ausgeführt.
The handyman carried out the repair quickly.
When it is about explaining, 'ausführen' (to elaborate) is often used with adverbs such as 'genauer' (more precisely / in more detail), 'detaillierter' (in more detail), or 'weiter' (further). It is a polite way to ask for more information.
Der Experte führte seine Gedanken zum Thema weiter aus.
The expert elaborated further on his thoughts about the topic.
In the meaning 'exportieren' (to export), 'ausführen' belongs to formal business or administrative language. It is often used in reports or official documents.
Das Unternehmen führt seit Jahren erfolgreich Maschinen nach Asien aus.
The company has been successfully exporting machines to Asia for years.
In this meaning, 'ausführen' (to take out) always requires an accusative object. The object is usually a person you take to a social event, or a pet for a walk.
Am Samstagabend hat er seine neue Freundin schick zum Essen ausgeführt.
On Saturday evening, he took his new girlfriend out for a fancy dinner.
to carry out
Durchführen and ausführen overlap when referring to planned work and assignments. Durchführen tends to emphasize the entire organized process. Ausführen focuses more on the concrete completion of an activity or instruction; depending on the context, either verb may fit.

Der Techniker führt den ersten Arbeitsschritt des Wartungsprogramms genau aus.
The technician carries out the first step of the maintenance program precisely.
Das Team führt das geplante Wartungsprogramm an der Anlage durch.
The team carries out the planned maintenance program on the system.