verify that the following is a solution to the biharmonic equation

F(x,y)=(Acosbx+Bsinbc+Cxcosbx+Dxsinbx)(Ecoshby+Fsi nhby)

i have tried taking the derivates and have gotten up to the laplacian but this is a very long and tedious way,and the result up to second order is really long, like a page long,there must be an easier way. Can someone suggest an alternative method to prove this