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ax to grind
ax to grind {n. phr.}, {informal}
Корыстная цель для того чтобы что-то заполучить.
In praising movies for classroom use he has an ax to grind; he sells motion picture equipment.
When Charles told the teacher he saw Arthur copying his homework from Jim, he had an ax to grind; Arthur would not let Charles copy from him.
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Источник: A Dictionary of American Idioms