Look at these examples:
Léo a reçu un vélo tout neuf pour son anniversaire.Leo received a brand new bike for his birthday.
J'ai acheté un nouveau vélo.I bought a new bike.
C'est une voiture d'occasion?
- Non, elle est neuve.Is it a second-hand car?
- No, it's new.
Emilie a trouvé sa nouvelle table au marché aux puces.Emilie found her new table at the flea market.
Notice that there is a nuance in French between neuf/neuve and nouveau/nouvelle.
While both mean 'new', neuf implies that it's never been used before, brand new (Note that it cannot apply to living things, e.g. pets), whereas nouveau just means 'new' in a more general sense.
In some context, obviously, both are correct.
However, the main difference of usage is the position in the sentence:
- neuf is placed AFTER the noun
- nouveau is placed BEFORE the noun
See also Beau, nouveau, vieux, fou, mou have two masculine forms and one feminine form (French Adjectives)
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