Unique rules when forming that grammar are highlighted like this
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Joining and Nesting Markers:
Verb[た/る] - means that dictionary form and ta form are accepted.
Verb[causative[て]] - means て form of the causative form of the verb.
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使用域一般
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てやる may be used ironically to show anger, or the strong resolve to perform undesirable actions to the listener (threatening), rather than performing favors for others sake. In addition it may also be used to express an intention to show off one's true ability/power. It’s often used together with expressions like どうせ、絶対、さっさと and the like.