Quadratic factor

Question

9n^2-9

 

How do I figure the answer?

Answer 1

9n² - 9 = (3n)² - 3²

 

This is a "difference of squares" of the form a² - b².  A difference of squares is always factored as follows

 

a² - b² = (a+b)(a-b)

 

You confirm that for yourself by multiplying out the (a+b)(a-b) using the FOIL method.  In your case, we have a = 3n and b = 3:

 

a² - b² = (a+b)(a-b)

 

(3n)² - 3² = (3n+3)(3n-3)