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Old English behofian "to have need of, have use for," verbal form of the ancient compound word represented by behoof.
Historically, it rimes with move, prove, but being now mainly a literary word, it is generally made to rime with rove, grove, by those who know it only in books. [OED]
c.1200, "use, benefit, advantage;" Old English had bihoflic "useful," implying *bihof "advantage, utility;" from Proto-Germanic *bi-hof "that which binds, requirement, obligation" (cf. Old Frisian bihof "advantage," Dutch behoef, Middle High German bihuof "useful thing," German Behuf "benefit, use, advantage"). In the common Germanic compound, the first element, likely intensive, is cognate with be- and the second with Old English hof, past tense of hebban "to raise" (see heave (v.)). The original sense is perhaps, then, "taking up (for oneself)."