In «ضَرَبَ الزَّيْدَانِ», the subject is an explicit noun, so the verb remains singular. In «الزَّيْدَانِ ضَرَبَا», the subject is the dual pronoun attached to the verb, so dual agreement appears. Likewise, compare «ضَرَبَ الزَّيْدُونَ» with «الزَّيْدُونَ ضَرَبُوا».
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Compare Explicit Nouns and Pronouns
Rules of the Fāʿil: Explicit Nouns, Pronouns, Number and Gender
In «ضَرَبَ الزَّيْدَانِ», the subject is an explicit noun, so the verb remains singular. In «الزَّيْدَانِ ضَرَبَا», the subject is the dual pronoun attached to the verb, so dual agreement appears. Likewise, compare «ضَرَبَ الزَّيْدُونَ» with «الزَّيْدُونَ ضَرَبُوا».