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to polish up; to shine up
職人は漆器を磨き上げた。
The craftsman polished the lacquerware until it gleamed.
彼女は技を磨き上げて完璧に踊った。
She refined her technique and danced perfectly.
彼は包丁の腕を磨き上げると決意した。
He resolved to polish up his knife skills.