都正确,homework或housework前的物主代词或定冠词都是可加可不加的。例如:
do (one's) homework《现代英汉综合大辞典》
do (the) housework《朗文当代英语词典》
1. I should help my parents with housework
2. I should help my parents with the housework
两句都对。第1句,泛指一般情况;第2句,特指具体的某些housework.
注意体会:
My parents are always very busy, so I should help my parents with housework.
My parents are ill today, so I should help my parents with the housework
《高考英语备考1号·速效编》
《高考英语备考1号·写作编》
《高中英语晨读晚记》
《高中英语错题笔记》
《零起点考大学英语》