Learn Dutch: Aangezien zij de offerte goedkeurden, zullen we het contract snel ondertekenen. - Since they approved the quote, we will sign the contract quickly.

Because aangezien (since/as) is a subordinating conjunction. Words like this introduce a dependent clause, which means they push the conjugated verb all the way to the end of their part of the sentence.

The verb for 'to approve' is the separable verb goedkeuren. Why isn't it split up here as 'zij keurden de offerte goed'?

In a normal main clause, a separable verb splits. However, because aangezien sends the verb to the end of the clause, the separated parts get pushed into the same spot, reunite, and are written together as one word: goedkeurden.

Why is the second half of the sentence structured as zullen we instead of we zullen?

This is due to the V2 (verb-second) rule. The entire first clause (Aangezien... goedkeurden) acts as the first block of information. To keep the main verb in the second position, zullen must come immediately after the comma, which pushes the subject (we) behind it.

Why is ondertekenen placed at the very end of the sentence rather than next to zullen?

The main clause uses the auxiliary verb zullen (will). In Dutch, an auxiliary verb or modal verb takes the second position, but it pushes the main action verb (ondertekenen) to the very end of the sentence in its full infinitive form.