neu
new
Describes something that was recently made, acquired, or created and has not yet been used, or has hardly been used.
Ich habe mir ein neues Fahrrad gekauft.
I bought myself a new bicycle.

new
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new
Describes something that was recently made, acquired, or created and has not yet been used, or has hardly been used.
Ich habe mir ein neues Fahrrad gekauft.
I bought myself a new bicycle.

'Neu' (new) is a very productive component of compound words. It is often found at the beginning of nouns and adjectives, where it always carries the meaning of 'new'.
Ein Neuanfang ist oft schwierig, aber auch eine große Chance.
A fresh start is often difficult, but also a big opportunity.
To emphasize that something is absolutely new and unused, you can use the colloquial intensifiers 'brandneu' (brand-new) or 'nagelneu' (brand-new / spick-and-span new).
Er hat sich ein brandneues Motorrad gekauft.
He bought himself a brand-new motorcycle.
To express that a person has only recently become part of a group or arrived at a place, 'neu' (new) is often used with the preposition 'in' (+ dative). Typical phrases are 'neu im Team' (new on the team) or 'neu in der Stadt' (new in town).
Unsere Nachbarin ist neu im Haus und kennt noch niemanden.
Our neighbor is new in the building and does not know anyone yet.
The expression 'von Neuem' is a fixed expression that means 'once again from the beginning.' It is used as an adverb and is not declined.
Sein Vortrag war so schlecht, dass er ihn von Neuem vorbereiten muss.
His presentation was so bad that he has to prepare it again from scratch.
different / differently
'neu' and 'anders' can both have to do with change. 'neu' emphasizes that something has only existed for a short time, has been introduced, or was previously unknown. 'anders' only emphasizes that something is not the same as before or not the same as something else. So a new plan can also be different, but not everything that is different is truly new. Learners often confuse the words because both fit situations involving changes. Ask yourself: Is it about something new, or only about a difference?

Im Restaurant gibt es heute ein neues Gericht auf der Karte.
Today there is a new dish on the menu at the restaurant.
Im Restaurant bestelle ich morgen etwas anders als sonst.
Tomorrow at the restaurant, I’ll order something different from usual.