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non-commutative algebra with formal functions

I'd like to look at the following: the set of formal functions with 2 variables f(x,y) and the real numbers a,b,c..., including an addition and a non-commutative multiplication, such that things like

expand((a+f(x,y))*(b+c*f(u,v))) = a*b + a*c*f(u,v) + b*f(x,y) + c*f(x,y)*f(u,v)

are possible (and vice versa), and with the multiplication of the functions

f(x,y)*f(u,v) != f(u,v)*f(x,y)

being non-commutative, however with the multiplication of the functions by the real scalars

a*f(x,y) == f(x,y)*a

still commutative. Can I construct something like that with sage?