zuschlagen
to strike
To hit something or someone with great force.
Der Einbrecher schlug mit der Faust zu, als er entdeckt wurde.
The burglar struck with his fist when he was discovered.

to strike / slam shut / snap up
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to strike
To hit something or someone with great force.
Der Einbrecher schlug mit der Faust zu, als er entdeckt wurde.
The burglar struck with his fist when he was discovered.

'Zuschlagen' is a separable verb. The prefix 'zu' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er schlug die Autotür laut zu.
He slammed the car door shut loudly.
To recognize the meaning 'to close something noisily', pay attention to an accusative object. If an object such as 'die Tür' (the door) or 'das Buch' (the book) is present, this meaning is intended, not hitting a person.
Sie schlug wütend den Laptop zu.
She angrily slammed the laptop shut.
In the meaning 'to take a buying opportunity', 'zuschlagen' (to snap up) is colloquial. It is typically used when talking about discounts, special offers, or bargains.
Bei diesem Preis für das Smartphone musste ich einfach zuschlagen.
At this price for the smartphone, I simply had to snap it up.
In the context of an auction, a special structure is used: the person who receives the winning bid is in the dative, and the auctioned item is in the accusative.
Der Auktionator schlug dem Sammler das seltene Buch zu.
The auctioneer knocked the rare book down to the collector.
When an amount is added to a price, it often appears with the preposition 'auf' and the accusative. This construction is also frequently used in the passive.
Auf den Grundpreis wird eine Servicegebühr zugeschlagen.
A service fee is added on to the base price.
to buy
'kaufen' and 'zuschlagen' can both occur in a buying situation. 'kaufen' is neutral and simply says that you get something in exchange for money. 'zuschlagen' is colloquial and here means that you take advantage of a good opportunity, especially with an offer or a good price. You do not use 'zuschlagen' for every normal purchase. Learners may confuse the words because the result is often the same: you buy something. The difference is the tone and the reason: 'zuschlagen' sounds like deciding quickly because the offer is good.

Weil der Laptop stark reduziert war, hat Anna sofort zugeschlagen.
Because the laptop was heavily reduced, Anna snapped it up immediately.
Bei den Eltern kauft Tom heute noch ein paar Sachen für seine neue Wohnung.
At his parents' place, Tom is buying a few more things for his new apartment today.