`f(x,y) = x^3 -4xy^2 + y^3` Determine whether the function is homogenous and if it is, determine its degree

Given,

`f(x,y) = x^3 -4xy^2 + y^3`

to check whether it is homogenous or not

`f(tx,ty)=(tx)^3 -4tx (ty)^2 + (ty)^3 = (t^3)(x^3 -4xy^2 + y^3)`

so this is of the form

`f(tx,ty)=t^n f(x,y)`

and so the function f(x,y) is homogenous,

`f(tx,ty)= (t^3)(x^3 -4xy^2 + y^3)`

and the Degree `n =3`