
ausarbeiten
to work out
To develop and create a plan, concept, text, or idea in detail and with care.
Das Team hat eine umfassende Strategie für das neue Projekt ausgearbeitet.
The team worked out a comprehensive strategy for the new project.
to work out / elaborate
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to work out
To develop and create a plan, concept, text, or idea in detail and with care.
Das Team hat eine umfassende Strategie für das neue Projekt ausgearbeitet.
The team worked out a comprehensive strategy for the new project.

to carve out
To shape or form something out of a material by working on it.
Der Bildhauer arbeitete die Figur detailgetreu aus dem Holzblock aus.
The sculptor carved the figure out of the block of wood in faithful detail.
'Ausarbeiten' (to work out/elaborate) is a separable verb. The prefix 'aus-' goes at the end in a main clause, remains attached to the verb in subordinate clauses, and in the infinitive with 'zu', 'zu' stands between 'aus' and 'arbeiten'.
Die Architektin arbeitet den Bauplan detailliert aus.
The architect works out the building plan in detail.
The verb is made up of the prefix 'aus-' and the verb 'arbeiten' (to work). Here, the prefix 'aus-' emphasizes that something is thought through or completed fully, in detail, and to the end.
Wir müssen die Präsentation bis morgen fertig ausarbeiten.
We have to finish working out the presentation by tomorrow.
In the meaning 'entwickeln' (to develop), 'ausarbeiten' (to work out) is often used with abstract concepts. Typical combinations are: 'einen Plan ausarbeiten' (to work out a plan), 'ein Konzept ausarbeiten' (to work out a concept), 'einen Vertrag ausarbeiten' (to draft a contract), or 'eine Rede ausarbeiten' (to prepare a speech in detail).
Die Anwälte haben den Vertrag gemeinsam ausgearbeitet.
The lawyers worked out the contract together.
When it is about craft or artistic shaping, the material from which something is made is often mentioned. Pay attention to the preposition 'aus' followed by a material in the dative.
Der Künstler arbeitete die feinen Gesichtszüge aus dem Marmorblock aus.
The artist carved the fine facial features out of the block of marble.
to develop
Both words can refer to creating a new idea or plan. „Entwickeln“ can include the idea’s creation and testing, while „ausarbeiten“ usually means developing an existing approach in detail and with care. „Entwickeln“ fits the entire creation process, while „ausarbeiten“ is more appropriate for the subsequent detailing.

Das Team arbeitet den vorhandenen Reiseplan mit genauen Zeiten und Wegen aus.
The team is working out the existing travel itinerary with exact times and routes.
Das Team entwickelt einen neuen Reiseplan und probiert verschiedene Möglichkeiten aus.
The team is developing a new travel itinerary and trying out various options.