SelectFree2[expr, a, b, ...] is similar to SelectFree but it also differs from the latter in several respects.
If expr is a list, SelectFree2 behaves exactly the same way as SelectFree.
If expr is not a list, SelectFree2 first expands the expression w.r.t. the arguments via Expand2.
Furthermore, SelectFree2[a,b] returns a and SelectFree2[a,a] returns 0. This differs from the behavior of SelectFree but is consistent with the naive expectations when applying the function to a sum of terms.
Overview, FreeQ2, SelectFree, SelectNotFree, SelectNotFree2.
Note the difference between SelectFree and SelectFree2
SelectFree[(a + b) c, b]c
SelectFree2[(a + b) c, b]a c
SelectFree[a, b]a
SelectFree2[a, b]a
SelectFree[a, a]1
SelectFree2[a, a]0
When there are hidden zeros, SelectFree2 obviously works better
SelectFree[(a - b + c)^2 - (a^2 - 2 a b + 2 a c + b^2 - 2 b c + c^2),a]-b^2+2 b c-c^2
SelectFree2[(a - b + c)^2 - (a^2 - 2 a b + 2 a c + b^2 - 2 b c + c^2),a]0