Hey all. I am having trouble factoring a question. If someone could explain how to go about doing this it would be very helpful!

Right, here is the question...

Factor Fully:

a^2 - p^2 +1 +2a

What I've done:

a^2 - p^2 +1 +2a

= (a + p)(a - p) + 1 +2a

unkown how to do the rest.

The answer in the book is: (a + 1 - p)(a + 1 + p). I've checked it and it works out.

Thank you in advanced!