Learn Farsi: طلا و نقره از زمین استخراج شد. - Gold and silver were extracted from the ground.

In Farsi, when the subject of a sentence is inanimate (not alive, like gold and silver), the verb is almost always in the singular form. That's why we use the singular شد instead of the plural شدند, even though there are multiple items.

How exactly does the passive voice work with a compound verb like استخراج کردن (to extract)?

To make a compound verb passive, you simply replace the "doing" part of the verb (کردن) with the "becoming" verb (شدن). So the active form "extracted" (استخراج کرد) becomes the passive form "was extracted" (استخراج شد).

The lesson says the passive uses a "past participle + shodan", but استخراج doesn't end like a normal past participle. Why?

Great observation! For regular verbs, you do use a past participle (like نوشته for "written"). However, for compound verbs made of an Arabic noun plus a helper verb (like استخراج کردن), you don't form a Farsi past participle. You just keep the noun part (استخراج) and pair it directly with the correct form of شدن.

Since gold and silver are the things being extracted, why isn't there the direct object marker را after them?

In a passive sentence, the thing that receives the action actually becomes the grammatical subject of the sentence. Because را is only used to mark specific direct objects, it disappears entirely when you change a sentence into the passive voice.