a) \({\rm{}}A + ({x^2} + {y^2}) = 5{{\rm{x}}^2} + 3{y^2} - xy\)
\(\eqalign{
& \Rightarrow A = (5{{\rm{x}}^2} + 3{y^2} - xy) - ({x^2} + {y^2}) \cr
& = 5{{\rm{x}}^2} + 3{y^2} - xy - {x^2} - {y^2} \cr
& = (5x^2-x^2)+(3y^2-y^2)-xy \cr
&= 4{{\rm{x}}^2} + 2{y^2} - xy \cr} \)
b) \(A - (xy + {x^2} - {y^2}) = {x^2} + {y^2}\)
\(\eqalign{
& \Rightarrow A = ({x^2} + {y^2}) + (xy + {x^2} - {y^2}) \cr
& = (x^2+x^2) + (y^2-y^2) + xy \cr&= 2{x^2} + xy \cr} \)
