我没看到上下文，这么看来应该是修饰cases的吧

肯定是three cases啊，好奇楼主的英语水平

cases = 复数, 所以该用 that illustrate, 不该用 which illustrate

引用回帖:

6楼: Originally posted by Gilbert_Liu at 2019-04-08 08:05:41
这句有语法错误？加拿大人的文献原文
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严格来说是有错, 但不要在意, 就像
  "Don't you know how to swim ?"
  "___, I don't know how to swim"
____ 内填  "Yes" 中学老师就扣分, 但日常英语常听到, 不那么明显罢了

高中英语最终目标是学改写:
  The method's underlying principles can be illustrated quickly using three distinct examples
句意和你的完全相同, quickly 表示不提供推导

真正的关键是 distinct 的含意
  The method's underlying principles can be illustrated quickly using three examples, each distinct in its....
  The method's underlying principles can be illustrated quickly using three examples, each distinguished by its...
改写方法很多, 最快的是介词切换

附注: methods, eah... 即可, 不需 methods, each of which
，

引用回帖:

6楼: Originally posted by Gilbert_Liu at 2019-04-08 08:05:41
这句有语法错误？加拿大人的文献原文
...

更正:

  examples, each... 即可, 不需 examples, each of which...