In a practice exam question, we are asked to find the Laplace transform solution of the 1D wave equation $\frac{\partial^2y}{\partial t^2}=c^2\frac{\partial^2y}{\partial x^2}$ obeying certain boundary conditions. It is a show-that question, and I was able to obtain the correct solution: $$Y(x,p)=\frac{a\sinh\left\lbrack\tfrac{p}{c}(L-x)\right\rbrack}{p\sinh(\tfrac{pL}{c})}.$$
The next part of the question is:
By use of the binomial theorem or otherwise, express $y(x,t)$ as an infinite series.
I have tried Taylor expanding and using the formula $(1-x)^{-1}=1+x+\dotsb$ (which I think is what they're hinting at with "binomial theorem") but to no avail...