Factorisation
Factorise is the inverse of expand where you put the brackets back into the equation. You need to look for the highest common factor (HCF) of both terms.
Note: for a recap on expand refer to Expand Brackets − 1
Note: for a more detailed recap on expand refer to Expand Brackets − 2
Note: for a recap on HCF refer to HCF
Example 1. Factorise 6a + 30
| 6a + 30 | | has the HCF of 6 |
| 6a + 30 | | = 6 × a + 6 × 5 |
| | | = 6 × (a + 5) |
| | | = 6(a + 5) |
Example 2. Factorise a + 3ab
| a + 3ab | | has the HCF of a |
| a + 3ab | | = a × 1 + a × 3b |
| | | = a × (1 + 3b) |
| | | = a(1 + 3b) |
Example 3. Factorise 4a + 20ab
| 4a + 20ab | | has the HCF of 4a |
| 4a + 20ab | | = 4a × 1 + 4a × 5b |
| | | = 4a × (1 + 5b) |
| | | = 4a(1 + 5b) |
Example 4. Factorise 14a + 63ab
| 14a + 63ab | | has the HCF of 7a |
| 14a + 63ab | | = 7a × 2 + 7a × 9b |
| | | = 7a × (2 + 9b) |
| | | = 7a(2 + 9b) |
to:
