
erweitern
to expand
To make something larger in size, area, or extent.
Die Firma plant, ihre Produktionshalle zu erweitern.
The company plans to expand its production hall.
to expand
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to expand
To make something larger in size, area, or extent.
Die Firma plant, ihre Produktionshalle zu erweitern.
The company plans to expand its production hall.

to expand
To enlarge something in terms of content or offerings by adding new elements or aspects.
Ich möchte meinen Horizont erweitern und eine neue Sprache lernen.
I want to expand my horizons and learn a new language.
The verb 'erweitern' (to expand) is derived from the adjective 'weit' (wide / far). The prefix 'er-' and the ending '-n' turn it into a verb that describes the process of making something 'weit' or 'weiter' (wider / further).
Die Stadt will das Netz der Fahrradwege erweitern.
The city wants to expand the network of bike paths.
The prefix 'er-' is inseparable. It remains directly attached to the verb stem in all sentence forms and tenses.
Er hat seine Sprachkenntnisse im Ausland erweitert.
He expanded his language skills abroad.
The object of the verb indicates the meaning. Concrete objects like 'Haus' (house) or 'Garten' (garden) mean an increase in area. Abstract objects like 'Wissen' (knowledge) or 'Angebot' (offerings) mean an expansion in content.
Wir müssen das Wohnzimmer um einen Anbau erweitern.
We need to expand the living room with an extension.
In a figurative sense, 'erweitern' (to expand) is very often used with abstract nouns such as 'Wissen' (knowledge), 'Kenntnisse' (skills / knowledge), 'Fähigkeiten' (abilities), or 'Horizont' (horizon).
Durch Reisen kann man seinen Horizont erweitern.
Traveling can expand your horizons.
to add / supplement
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 erweitern den Bericht um ein Kapitel über die neuen Ergebnisse.
We are expanding the report by adding a chapter on the new findings.
Wir ergänzen den Bericht um die noch fehlenden Zahlen.
We are supplementing the report with the figures that are still missing.