Simplification into a specific form



I have a rather lengthy function of several variables that I know simplifies
into a particular form. An over-simplified version of the problem goes like
this. Suppose I know a function of x and y simplifies into the form

a*(x + y)^2 + b*(x^2 + y^2)

where a and b are constants. If maxima has the function in the form

2*(x^2 + y^2 + x*y)

how can I get it to give me it in the desired form? That is, how do I
get maxima to tell me that a=1 and b=1?

Any suggestions would be appreciated.

Jim Schott