Difference of the square - Tricky question for me...

Hi ! First post here !

I'm having some difficulty with a math problem in my math book and I'm starting to think the author made a mistake.

I'm trying to factorize using the "difference of the squares" technique. According to my book, it should result in the following factors :

Now, if I multiply those two factors together, it gives me this :

then

so, I'm tempted to conclude that does not equal , and therefore that my book is wrong about it.

Am I right ? Did I make a mistake ?