やる・〜てやる
give / do (for someone lower); I'll show you
Noun に + Noun を + やる · Verb て-form + やる
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やる is a casual form of あげる, used for giving to people or animals below you: 犬にえさをやる, "feed the dog"; 花に水をやる, "water the flowers".
てやる does the same for favours: 弟に宿題を教えてやった, "I helped my little brother with his homework". It's fine for younger family members, pets and plants, but with adults it sounds condescending; use てあげる instead.
It also expresses determination or a threat, often in anger: 絶対に勝ってやる, "I'll win, just you watch".
Remember the direction: やる and あげる go out from you; くれる comes to you.
Examples
犬にえさをやりました。
I fed the dog.
毎朝、花に水をやる。
I water the flowers every morning.
弟に宿題を教えてやった。
I helped my little brother with his homework.
今度こそ、絶対に勝ってやる。
This time, I'll win, just you watch.
子どもに絵本を読んでやった。
I read my child a picture book.