1610s, "anything spread out;" 1640s, "act of expanding," from French expansion, from Late Latin expansionem (nominative expansio) "a spreading out," noun of action from past-participle stem of Latin expandere "to spread out, unfold, expand," from ex "out" (see ex-) + pandere "to spread, stretch" (from nasalized form of PIE root *pete- "to spread").
the expansion of (a+b)^2 is a^2 + 2ab + b^2
exothermic
exotic
exoticism
expand
expanse
expansion
expansionist
expansive
expat
expatiate
expatiation