桃李满天下 Peach and plum trees cover the whole country
Explanation
这个成语形容老师的学生很多，遍布各地，就像满山遍野的桃树和李树一样。
This idiom describes a teacher who has many students scattered all over the place, like peach and plum trees covering the whole landscape.
Origin Story
汉代名臣杨震，以廉洁著称，他当官时，从不收受贿赂，曾有人送他金子，杨震严词拒绝，并告诫来人：“此乃“腐鼠”也，不可沾之”。杨震的清廉正直，感动了许多人，他们都愿意向他学习，在他的教导下，很多人都成为了栋梁之材，所以人们常说“天下桃李，悉在公门矣”，来形容杨震培养了众多人才，遍布朝堂。
Yang Zhen, a famous minister of the Han dynasty, was known for his integrity. During his time as an official, he never accepted bribes. Once, someone offered him gold, but Yang Zhen firmly refused, warning the person: “This is like a ‘rotten rat’, you can’t touch it.” Yang Zhen’s integrity and righteousness touched many people, who were willing to learn from him. Under his guidance, many became pillars of the state. Therefore, people often say “天下桃李，悉在公门矣”, to describe how Yang Zhen nurtured numerous talents who filled the court.
Usage
多用于赞扬老师培养的学生众多，桃李满天下，形容老师教书育人的伟大成就。
It is often used to praise the many students that a teacher has trained. 桃李满天下, describes the great achievements of a teacher in training students.
Examples
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他桃李满天下，学生遍布全国。
ta tao li man tian xia, xue sheng bian bu quan guo.
He has students all over the country.
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这位老先生桃李满天下，深受学生的爱戴。
zhe wei lao xian sheng tao li man tian xia, shen shou xue sheng de ai dai.
This old man has students all over the world, he is deeply loved by his students.
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这位老师桃李满天下，培养了无数人才。
zhe wei lao shi tao li man tian xia, pei yang le wu shu ren cai
This teacher has students all over the world, he has cultivated countless talents.