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Phrase(s): extend one’s sympathy (to someone)
to express sympathy to someone. (A very polite and formal way to tell someone that you are sorry about a misfortune.) • Please permit me to extend my sympathy to you and your children. I’m very sorry to hear of the death of your husband. • Let’s extend our sympathy to Bill Jones, who is in the hospital with a broken leg. We should send him some flowers.
McGrawhill's American Idioms And Phrasal Verbs