FCSplit[exp, {v1, v2, ...}] splits expr into pieces that
are free of any occurrence of v1, v2, ... and pieces that
contain those variables. This works both on sums and products. The
output is provided in the form of a two element list. One can recover
the original expression by applying Total to that list.
FCSplit[(a + b)^2, {a}]\left\{b^2,a^2+2 a b\right\}
FCSplit[(a + b + c)^2, {a, b}]\left\{c^2,a^2+2 a b+2 a c+b^2+2 b c\right\}