beschmieren
to smear
To apply or spread something, often a sticky, dirty, or colored substance, messily and over a surface.
Das Kind hat die Wand mit Schokolade beschmiert.
The child smeared chocolate on the wall.

to smear / deface
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to smear
To apply or spread something, often a sticky, dirty, or colored substance, messily and over a surface.
Das Kind hat die Wand mit Schokolade beschmiert.
The child smeared chocolate on the wall.

'Beschmieren' (to smear / deface) is an inseparable verb with the prefix 'be-'. The prefix remains firmly attached to the verb 'schmieren' (to smear) in all tenses and sentence types.
Er hat die ganze Tischdecke mit Marmelade beschmiert.
He smeared the entire tablecloth with jam.
The construction is always: someone 'beschmiert' (smears) SOMETHING (accusative) 'mit' SOMETHING (dative). The surface is the accusative object, and the substance is attached with 'mit' + dative.
Die Kinder haben den Spiegel mit Zahnpasta beschmiert.
The children smeared the mirror with toothpaste.
The word 'beschmieren' (to smear / deface) always has a negative connotation. It means making something messy, dirty, or ugly.
Nach dem Spiel war sein Trikot komplett mit Schlamm beschmiert.
After the game, his jersey was completely smeared with mud.
In this meaning, the substance usually refers to paint, spray paint, or writing. Typical objects are walls, outer walls, trains, or monuments.
Leider wurde die frisch gestrichene Wand über Nacht mit Graffiti beschmiert.
Unfortunately, the freshly painted wall was defaced with graffiti overnight.
to spread / to grease / to bribe
'schmieren' and 'beschmieren' both have to do with applying or spreading something messily. 'schmieren' can be neutral, for example 'Butter aufs Brot schmieren' (to spread butter on bread), or negative when something is written or painted messily. 'beschmieren' usually sounds negative: a surface becomes dirty, sticky, or is painted on in an unwanted way. Especially with walls, tables, or doors, 'beschmieren' is more natural when something is being spoiled or defaced as a result. Learners may confuse the words because both describe a similar movement. The important point is: 'beschmieren' puts stronger emphasis on the bad result on the surface.

Am Abend haben Unbekannte die Wand am Bahnhof beschmiert.
In the evening, unknown individuals defaced the wall at the train station.
Zum Frühstück schmiert Lisa Butter auf ihr Brot.
For breakfast, Lisa spreads butter on her bread.