If a polynomial can be written as a2 – b2, then it can be factored as a difference of squares:
a2 – b2 = (a + b)(a – b)
This is because, when you use FOIL to expand the right side, the ab terms cancel out:
(a + b)(a – b) = a2 – ab + ab – b2
Factor, if possible.
9p2 – 49q2
This is a difference of squares with a = 3p and b = 7q.
9p2 – 49q2 = (3p – 7q)(3p + 7q)
You should verify this using FOIL.