difference of two squares
Some expressions factor on sight once you learn the pattern. A difference of two squares is anything shaped like (something)^2 minus (something else)^2, and it always factors into the sum times the difference of those two things: a^2 - b^2 = (a + b)(a - b). The two middle terms cancel when you multiply back out, which is why it works so cleanly.
The skill is recognizing the pattern in disguise. x^2 - 25 is x^2 - 5^2 = (x + 5)(x - 5). Likewise 9y^2 - 16 is (3y)^2 - 4^2 = (3y + 4)(3y - 4). The two requirements are that both pieces are perfect squares and that they are subtracted, not added.
Crucially, a SUM of two squares, a^2 + b^2, does NOT factor over the real numbers — it has no real roots, so there is no real version of this pattern for addition. (It does factor using complex numbers, but that is a separate world.) Whenever you see a plus sign between two squares, do not force this rule.
49 - x^2 = 7^2 - x^2 = (7 + x)(7 - x).
Two perfect squares, subtracted, factor as sum times difference.
A common beginner error is to 'factor' a^2 + b^2 as (a + b)^2. That is wrong: (a + b)^2 = a^2 + 2ab + b^2, which has an extra middle term. Over the reals, a^2 + b^2 is prime.