c. 1300, "unfold, spread out, unfurl" (a banner, etc.), from Old French desploiir (Modern French déployer) "unfold, unfasten, spread out" (of knots, sealed letters, etc.), from Latin displicare "to scatter," in Medieval Latin "to unfold," from dis- "un-, apart" (see dis-) + plicare "to fold" (from PIE root *plek- "to plait").
Properly of sails or flags (and unconnected to play); meaning "reveal, exhibit, expose to view" is late 14c.; sense of "reveal unintentionally, allow to be seen" is from c. 1600. Related: Displayed; displaying.
mid-15c., "occupying time, made longer," past-participle adjective from extend (v.). Meaning "stretched out" in space is from 1550s; extended-play (adj.), in reference to recordings (especially 7-inch, 45 rpm vinyl records) is from 1953; in reference to pinball games by 1943. Extended family (n.) in sociology recorded from 1942.
A challenging question was asked RCA engineers and scientists in 1951. How can we increase the playing time of a 7-inch record, without using a larger disc? Sixteen months of research gave the answer, "45 EP"—Extended Play. [Radio Corporation of America magazine advertisement, May 1953]