Expanding

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Expanding takes an expression written as a product, like (x+1)*(x+2), and multiplies it out into a sum of terms. It is the everyday algebra of removing brackets, done for you. Unlike symbolic evaluation, this does not need a trailing arrow: asking to expand something already says its unknowns are meant to stay unknown.

expand multiplies out every product and power, then collects like terms.

expand((x+1)*(x+2)) // x^2+3x+2
expand((x+1)^3) // x^3+3x^2+3x+1
expand((x+y)^2) // x^2+2x*y+y^2

Terms come out in descending degree, so an expression always reads the way it is conventionally written and two equal expressions always render identically.

What expanding does not do

expand leaves anything that is not a polynomial alone rather than reporting an error, since there is nothing to multiply out but nothing wrong either.

expand(sin(x)) // sin(x)

Division by an unknown makes an expression a rational function rather than a polynomial, so it is also left as written.

expand(x/y + 1) // x/y+1