# Another question from Gelfand and Shilov, Generalized function vol I.

So in page 258, how to arrive at Eq (25)?:

$$LP^{\lambda +1} = 2(\lambda +1)(2\lambda +n) P^{\lambda}$$

where $$L=P(\frac{\partial}{\partial x_1},\cdots , \frac{\partial}{\partial x_{p+q}})=\frac{\partial^2}{\partial x_1^2}+\cdots + \frac{\partial^2}{\partial x_p^2}-\frac{\partial^2}{\partial x_{p+1}^2}-\cdots - \frac{\partial^2}{\partial x_{p+q}^2}$$

After I open the brackets for $(\frac{\partial^2}{\partial x_1^2}+\cdots + \frac{\partial^2}{\partial x_p^2}-\frac{\partial^2}{\partial x_{p+1}^2}-\cdots - \frac{\partial^2}{\partial x_{p+q}^2})^{\lambda +2}$

I get mixed derivaative which I don't know how to eliminate them. They write that it's a simple calculation, and I am clueless... :-(