# Math Help - Factoring Help - reorganizing terms and grouping?

1. ## Factoring Help - reorganizing terms and grouping?

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!

2. Originally Posted by Xenophobe
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!
You first need to re-arrange: $a^2 - p^2 + 1 + 2a = a^2 + 2a + 1 - p^2 = (a + 1)^2 - p^2 = \, ....$

3. Originally Posted by mr fantastic
You first need to re-arrange: $a^2 - p^2 + 1 + 2a = a^2 + 2a + 1 - p^2 = (a + 1)^2 - p^2 = \, ....$
In case you were wondering where to go from here...

Difference of squares ought to do it.