
ergänzen
to add
To add something missing in order to make something whole or complete.
Bitte ergänzen Sie die fehlenden Angaben im Formular.
Please add the missing information to the form.
to add / supplement
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to add
To add something missing in order to make something whole or complete.
Bitte ergänzen Sie die fehlenden Angaben im Formular.
Please add the missing information to the form.

to complement each other
Two or more people or things go well together and complete each other in their qualities or abilities.
In unserem Team haben wir unterschiedliche Stärken und ergänzen uns daher perfekt.
In our team, we have different strengths and therefore complement each other perfectly.

to add
To add additional information or a comment to something that has already been said or written.
Ich möchte noch ergänzen, dass die Frist bereits morgen abläuft.
I would also like to add that the deadline is already tomorrow.
The verb 'ergänzen' (to add/supplement) is derived from the adjective 'ganz' (whole). The prefix 'er-' and the ending '-en' turn it into a verb that literally means to make something 'ganz' (whole) or complete.
Könnten Sie Ihre Sammlung um dieses seltene Buch ergänzen?
Could you supplement your collection with this rare book?
In the meaning 'Fehlendes hinzufügen' (to add what is missing), 'ergänzen' (to add) is often combined with nouns such as 'Liste' (list), 'Sammlung' (collection), 'Daten' (data), or 'Angaben' (information/details).
Bitte ergänzen Sie die fehlenden Daten in der Tabelle.
Please add the missing data to the table.
When people or things complete each other, the verb is used reflexively: 'sich ergänzen' (to complement each other). It is often intensified by adverbs such as 'gut' (well), 'perfekt' (perfectly), or 'gegenseitig' (mutually).
Die beiden Musiker ergänzen sich auf der Bühne perfekt.
The two musicians complement each other perfectly on stage.
To add additional information in a conversation or presentation, the phrase 'Ich möchte (noch) ergänzen, dass ...' (I would like to add that ...) is often used. It is followed by a subordinate clause.
Ich möchte ergänzen, dass wir für diese Aufgabe mehr Zeit benötigen.
I would like to add that we need more time for this task.
to expand
Erweitern makes a text or an offering larger by adding new content or components, without anything specific necessarily being missing. Ergänzen, by contrast, usually adds a missing aspect or provides additional information. Use erweitern for greater scope and ergänzen for greater completeness.

Wir ergänzen den Bericht um die noch fehlenden Zahlen.
We are supplementing the report with the figures that are still missing.
Wir erweitern den Bericht um ein Kapitel über die neuen Ergebnisse.
We are expanding the report by adding a chapter on the new findings.