$9a^2-a^4+2a^2b-b^2 $ how to factor this algebraic expression? Algebraic identities

Question

I can't match any of the most common algebraic identities with this expression.

$9a^2-a^4+2a^2b-b^2 $

Once this algebraic expression is factored this should come out

$ (3a-a^2+b)(3a+a^2-b)$

Can someone tell me the name of the algebraic identity that you use to factor/rewrite this expression and how you have solved it?

Answer 1

Hint:

Separate the $9a^2$ out and focus on the remaining three terms:

$-(a^4-2a^2b+b^2)$

Allowing $u = a^2$ might make the algebraic identity (something to do with binomials) more visible. Move on from there.