Difference of two squares, step by step

Something squared minus something squared is the sum times the difference.

The question

x² − 900

x² = (x)²900 = 30²

(x + 30)(x − 30)

x² − 900=(x + 30)(x − 30)

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 900 is 30 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 + 30)(x − 30).
So the missing number is 30: 900 is 30 squared, so the two brackets are (x + 30) and (x − 30).

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 900 is 30 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 + 30)(x − 30).
03
So the missing number is 30: 900 is 30 squared, so the two brackets are (x + 30) and (x − 30).