variieren
to vary
To differ or occur in different forms or versions.
Die Preise für Hotelzimmer variieren stark je nach Saison.
The prices for hotel rooms vary greatly depending on the season.

to vary
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to vary
To differ or occur in different forms or versions.
Die Preise für Hotelzimmer variieren stark je nach Saison.
The prices for hotel rooms vary greatly depending on the season.

Verbs ending in '-ieren' often come from other languages and are always regular. They form the past participle without 'ge-'. So it is 'hat variiert' (has varied).
Der Koch hat das klassische Rezept etwas variiert.
The cook varied the classic recipe a little.
'Variieren' can be used with or without an accusative object. Without an object, it means that things are different by themselves. With an object, it means that someone actively changes something.
Die Meinungen zu diesem Thema variieren stark.
Opinions on this topic vary greatly.
When something differs by itself, 'variieren' is often used with words such as 'Preise' (prices), 'Größen' (sizes), 'Temperaturen' (temperatures), or 'Qualität' (quality). Common adverbs are 'stark' (greatly), 'leicht' (slightly), or 'je nach' (depending on).
Die Qualität der Produkte kann von Hersteller zu Hersteller variieren.
The quality of the products can vary from manufacturer to manufacturer.
To indicate the reason for a variation, the construction 'je nach' (depending on) followed by a noun in the dative is often used.
Die Lieferzeiten variieren je nach Bestimmungsort.
Delivery times vary depending on the destination.
to change
'verändern' and 'variieren' can both mean that something does not always stay the same. 'verändern' is more general and can mean a clear change or transformation. 'variieren' is used more when there are several versions or small variations. It fits well when you want to create variety, for example with exercises, recipes, or music. Learners may confuse the words because both have to do with change. As a simple guide: 'verändern' emphasizes becoming different, while 'variieren' emphasizes different possibilities.

Kannst du die Übungen variieren, damit das Training nicht langweilig wird?
Can you vary the exercises so the training doesn't get boring?
Ich verändere bei der Arbeit meinen Tagesplan, wenn ein wichtiger Termin dazukommt.
I change my daily schedule at work when an important appointment is added.