Two dimensional Taylor Series Linear Approximation

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Hi so I'm Currently studying Multivariable Calculus and Real Analysis and have came to a wall on this question. I know from reading my notes that I have to find F(x,y), Fx(x,y), Fy(x,y), Fxx(x,y), Fyy(x,y) and, Fxy(x,y) for the first steps and then sub in the point (3,2) into each answer but I'm unsure on how to find the final expression as I don't know where some terms are coming from. Is there a step by step solution or is it different for each function?