die Ausarbeitung
elaboration
The process by which a plan, concept, or text is developed and formulated in detail.
Die Ausarbeitung des neuen Vertrags hat mehrere Wochen gedauert.
The elaboration of the new contract took several weeks.

elaboration / paper
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elaboration
The process by which a plan, concept, or text is developed and formulated in detail.
Die Ausarbeitung des neuen Vertrags hat mehrere Wochen gedauert.
The elaboration of the new contract took several weeks.

The noun 'die Ausarbeitung' (elaboration/paper) is derived directly from the separable verb 'ausarbeiten' (to work out/elaborate). The ending '-ung' turns the verb into a feminine noun that can describe both the process and the result.
Wir müssen dieses Konzept noch genauer ausarbeiten.
We still need to work out this concept in more detail.
Whether the process (meaning 1) or the finished document (meaning 2) is meant can often be recognized from the verb. Verbs like 'dauern' (to take/last) or 'beginnen' (to begin) point to the process, while verbs like 'abgeben' (to hand in) or 'lesen' (to read) point to the result.
Die Ausarbeitung des Businessplans dauerte drei Monate.
The elaboration of the business plan took three months.
The word 'Ausarbeitung' (elaboration/paper) is used very frequently in academic, professional, or administrative contexts. It sounds more formal and precise.
Für das Seminar ist eine schriftliche Ausarbeitung zu einem Thema Ihrer Wahl erforderlich.
For the seminar, a written paper on a topic of your choice is required.
When 'Ausarbeitung' (paper/write-up) means the finished document, it is often combined with verbs such as 'einreichen' (to submit), 'vorlegen' (to present/submit), 'präsentieren' (to present), or 'verfassen' (to write).
Die Studenten müssen ihre Ausarbeitungen bis Freitag einreichen.
The students must submit their papers by Friday.
work
'die Arbeit' and 'die Ausarbeitung' can both have to do with a written assignment or a project. 'die Arbeit' is more general and can mean the task, the text, or even the activity itself. 'die Ausarbeitung' more specifically means the detailed development of a plan, concept, or text, or the finished result of that process. Learners may confuse the words because both can be used for a written result. 'Arbeit' sounds more neutral and broader. 'Ausarbeitung' fits especially when something has been thoroughly developed, structured, and precisely formulated.

Vor dem Termin ist Davids Ausarbeitung noch nicht ganz fertig.
Before the appointment, David's write-up is not quite finished yet.
Im Zug liest Anna ihre Arbeit noch einmal durch.
On the train, Anna reads through her paper one more time.