expand

Spreading has turned into scope here. What grows is reach or count, not physical size. Milton's "expanded wings" in Paradise Lost (1667) still carries the old spreading image. The 1961 article "The winter timetables of British Railways" uses the newer one, reporting that two trains each way "have been expanded to four". Typical objects are operations, services and offerings. The intransitive partner drops the object entirely.

The physical sense the others grow from. English has used it since 1422, as Middle English expanden, from Latin expandere, "to spread out", built from ex- "out" and pandō "to spread". That spreading is still audible when a map or an umbrella is opened flat rather than merely enlarged. Spawn is an unexpected cousin: it is a doublet, the same Latin word reaching English by a different road.

A single compact umbrella shows the switch. You can expand it, or it expands to cover a large table. Without an object, the growing thing moves into subject position, which suits statements about how matter behaves: many materials expand when heated. When someone does the enlarging, reach for the spreading-out meaning instead.

Modern English almost always adds a preposition: expand on a point, expand upon an argument. Stephen Crane could still write in Twelve O'Clock (1899) that a character was "left free to expand his ideas", with no on at all. That shape now reads as older prose. Learners are safest with on, which also marks the sense apart from physical growth.

An interface verb that always comes paired with its opposite: whatever can be expanded can be collapsed again. The object is the parent item, not what lies beneath it. You expand a folder to see its files, or a heading to see its subheadings. Nothing actually grows here, because the hidden levels were there all along. The older idea of laying something open, as in the spreading-out sense, fits it better than enlargement.

The binomial theorem is the classic tool for this job: it turns (x + 1)⁴ into a full row of terms without multiplying it out by hand. The operation runs opposite to factoring, which packs a sum back into a product. The two work as a pair: expand to see every term, factor to see the structure. Either way, the value never changes.

Here the expression itself is the subject, and the construction is expands to: (x + 1)⁴ expands to x⁴ + 4x³ + 6x² + 4x + 1. It states the result without naming anyone who did the rewriting. Use the transitive rewriting sense for the instruction (expand the product) and this one for the outcome.

Arithmetic borrows the word for a step that changes how a fraction looks but not what it is worth: expanding 4/7 by 3 gives 12/21. The construction is expand by, which names the multiplier. It reverses reducing to lowest terms, and it is how unlike fractions are brought to a common denominator. Unlike the algebraic sense, nothing turns into a sum.