Given an expression like
a + b*y + c*y^2 + d*Sqrt[f + g*y + h*y^2]
How can I programatically, expand this to a quartic without any fractional powers?
Right now, I am having to copy and paste it as input expression and manually move the Sqrt to the RHS and square. I suspect there's an easier way to do this in Mathematica, perhaps using the Coefficient function or something similar.