Factor a difference of squares, step by step

x² − 64 is one square minus another, and it factors on sight into (x + 8)(x − 8).

The question

x² − 225

x² = (x)²225 = 15²

(x + 15)(x − 15)

x² − 225=(x + 15)(x − 15)

Before factoring anything, check the shape. There are two parts with a − between them, and each part has to be a perfect square: x² is x squared, and 225 is 15 squared. Both are, and it is a minus — so this is a difference of two squares.
That shape always factors the same way, and there is nothing to search for: it is the SUM times the DIFFERENCE of the two things being squared — (x + 15)(x − 15).
So the missing number is 15: 225 is 15 squared, so the two brackets are (x + 15) and (x − 15).

How it works.

01
Before factoring anything, check the shape. There are two parts with a − between them, and each part has to be a perfect square: x² is x squared, and 225 is 15 squared. Both are, and it is a minus — so this is a difference of two squares.
02
That shape always factors the same way, and there is nothing to search for: it is the SUM times the DIFFERENCE of the two things being squared — (x + 15)(x − 15).
03
So the missing number is 15: 225 is 15 squared, so the two brackets are (x + 15) and (x − 15).