scheren
to shear
To cut the wool off sheep or the hair off other animals with shears or a clipper.
Im Frühling werden die Schafe auf der Weide geschoren.
In spring, the sheep in the pasture are sheared.

to shear / to care
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to shear
To cut the wool off sheep or the hair off other animals with shears or a clipper.
Im Frühling werden die Schafe auf der Weide geschoren.
In spring, the sheep in the pasture are sheared.

The verb 'scheren' (to shear) is the basis for the noun 'die Schere' (scissors). The basic meaning is a cutting motion with two blades.
Mit dieser alten Schere kann man kaum noch Papier schneiden.
You can barely cut paper with these old scissors anymore.
This reflexive expression has a fixed structure: 'sich um etwas scheren' (to care about something). It is almost always negated to express indifference. Pay attention to the reflexive pronoun and the preposition 'um' with the accusative.
Ich schere mich nicht darum, was die Nachbarn sagen.
I don't care about what the neighbors say.
In this meaning, 'sich scheren' is colloquial and rude. It is usually used as a command in the imperative to send someone away.
Scher dich hier raus, ich will dich nicht mehr sehen!
Get out of here; I don't want to see you anymore!
The grammatical form helps distinguish the meanings: the reflexive forms 'sich um etwas scheren' (to care about something) and 'sich scheren' (to go away) are clearly separate from the non-reflexive form with an object, such as 'Schafe scheren' (to shear sheep) or 'Blech scheren' (to shear sheet metal).
Der Bauer schert seine Schafe jedes Jahr im Mai.
The farmer shears his sheep every year in May.
to separate
'trennen' and 'scheren' can both have to do with something being divided by cutting or a similar action. 'trennen' is much more general: you can separate paper, fabric, or other things into parts. 'scheren' is used especially when cutting off wool or animal hair, for example from sheep. In technical contexts, 'scheren' can also mean cutting metal or other material with blades. Learners may confuse the words because both describe a kind of cutting apart. In everyday language, however, 'scheren' is much more specific than 'trennen'.

Im Frühling schert der Bauer die Schafe auf der Wiese.
In spring, the farmer shears the sheep in the meadow.
Mit einer Schere trennt Lisa den Stoff in zwei gleich große Stücke.
Lisa uses scissors to cut the fabric into two equal-sized pieces.