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|Expand[expr]||multiply out products and powers, writing the result as a sum of terms|
|Factor[expr]||write expr as a product of minimal factors|
Expand gives the "expanded form", with products and powers multiplied out.
Factor recovers the original form.
It is easy to generate complicated expressions with Expand.
Factor often gives you simpler expressions.
There are some cases, though, where Factor can give you more complicated expressions.
In this case, Expand gives the "simpler" form.