What it means
てやる expresses doing something for another person, usually someone younger, subordinate, or very close to the speaker. It has a familiar and sometimes rough tone, and the speaker often emphasizes that they will take the action for the other person. The neutral polite counterpart is てあげます, which is the polite form of てあげる rather than a simple polite form of the rough てやる.
Usage note
てやる can sound condescending or aggressive when used toward equals, superiors, customers, or people outside the speaker's close circle. In those situations, てあげる or the polite てあげます is usually safer. Do not confuse this pattern with てくれる, which describes someone doing something for the speaker or the speaker's group.
How to use it
私は妹に自転車の乗り方を教えてあげます。
I will teach my younger sister how to ride a bicycle.
私は妹に自転車の乗り方を教えてやる。
I will teach my younger sister how to ride a bicycle.
Example sentences
弟が宿題で困っているから、数学の問題を一緒に解いてやる。
Because my younger brother is having trouble with his homework, I will solve the math problems together with him.
子犬が寒そうだから、古い毛布をかけてやる。
The puppy looks cold, so I will cover it with an old blanket.
甥が重い荷物を運