Lesson 2 of 3
SHORTCUT
Something squared minus something squared factorises on sight.
The question
Factorise 49x² − 16
a² − b² = (a + b)(a − b). Take the square root of each part, then write one bracket with a plus and one with a minus.
So: (7x + 4)(7x − 4)
Same two things, one bracket smiling and one frowning. Only ever works with a minus in the middle.
This only applies to a *difference*. a² + b² does not factorise over real numbers, and writing brackets for it loses marks. Also check for a common factor first: 2x² − 18 must become 2(x² − 9) before you use the identity.
Expanding (a+b)(a−b) gives a² − ab + ab − b². The two middle terms cancel exactly, leaving only a² − b².
Factorise x² − 9
Factorise 25x² − 1
Factorise 4x² − 49
