Factorising x2 − a2
x2 − a2 can be factorised to (x + a)(x − a). The inverse of this is Quadratic Expansion − Difference of two squares
Note: for a recap on Quadratic Expansion refer to Quadratic Expansion
Example 1. Factorise x2 − 25
Example 2. Factorise a2 − 36
Example 3. Factorise 100x2 − 144
Example 4. Factorise 4x2 − 49a2
| x2 − 25 | = x2 − 52 | |
| = (x + 5)(x − 5) |
| a2 − 36 | = a2 − 62 | |
| = (a + 6)(a − 6) |
100x2 − 144
| = (10x)2 − 122 | ||
| = (10x + 12)(10x − 12) |
4x2 − 49a2
| = (2x)2 − (7a)2 | ||
| = (2x + 7a)(2x − 7a) |
to: 
