Question

The girl with her little brothers _is taken_good care of by the teachers in this special school.

为什么横线部分要用is加过去分词，不是are加过去分词吗?

Answer 1

这里考的是with,的用法 主谓一致中的靠前原则即：
后面的【谓语动词的单复数 取决于with 前面的主语的单复数情况】
这里的主语是the girl所以谓语用is
可以将其改为the girl【 is 】taken good care of by the teachers in this special school 【with her little brothers】
还有一些词语也遵守靠前原则 它们是：
together with,like,except,but,no less than,as well as连接两个主语用靠前原则。
例如：Mary as well as you is my friend.
The teacher together with some students is visiting the factory.这里的 with

Answer 2

这里的with相当于补充成分，你可以把with her little brothers 这个成分直接挪到后面去不管，谓语动词根据主语the girl 来确定。

Answer 3

is是就girl而言的，with her brothers是一个附加成分，可以后移
也就是说这句话可以是the girl is taken good care of by the teachers in this special school with her little brothers.

Answer 4

这里with her little brothers是附带的，主语是the girl，所以用单数
这里女孩和她的小弟弟们被这所特殊学校的老师照顾得很好

Answer 5

因为主语是the girl, 后面虽然带了她的Little brothers,但从语法角度讲，用With连接时状态修饰词. 所以主语还是单数.