Examples:

Factor the following:

1) 9 - r2

   From the form (a2x2 - b2) = (ax + b)(ax - b),
   a2 = 1, thus a = 1
   x2 = 9, thus x = 3
   b2 = r2, thus b = r,  in this case.

   Therefore, (a2x2 - b2) = (3 + r)(3 - r).
   Thus,  9 - r2 = (3 + r)(3 - r).

 2) 9p2 - 4
    
    a2 = 9, thus a = 3
    x2 = p2, thus x = p
    b2 = 4, thus b = 2,  in this case.  
   
    Therefore, (a2x2 - b2) = (3p + 2)(3p - 2).
    Thus,  9p2 - 4 = (3p + 2)(3p - 2).

    Note:  you can also use the decomposition method on expressions like these
    but you have to add the linear term into the expression with a coefficient
    of zero. (i.e. 4x2 - 9 = 4x2 + 0x - 9.  Now, the 0x term can be slpit 
    into (-6x) + (6x).  Performing the decompostion method on the new expression:
    4x2 - 6x + 6x - 9, results in (2x + 3)(2x - 3).

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