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Does this :

sage: var("a b c x y")
(a, b, c, x, y)
sage: foo =  a*x^2 + a*y^2 + b*y^2 + c*y^2 + (2*a*y + b*y)*x
sage: sum([u*foo.coefficient(u) for u in (x^2, y^2, x*y)])
a*x^2 + (2*a + b)*x*y + (a + b + c)*y^2

answer your question ?

HTH,