Factorising an expression involves identifying common factors in the expression, then creating brackets and putting the factors outside the brackets. A common factor can be a number or a letter, or a combination of numbers and letters. It is the opposite of expanding an expression.
An example is to factorise `3x + 9`. The number 3 divides into both the 3 (of `3x`) and the 9. Create a pair of brackets, and put the common factor outside the brackets, gives:
`3x + 9 = 3(x + 3)`
Factorising `9ab + 12b` has both 3 and `b` as factors:
`9ab + 12b = 3b(3a + 4)`
because 3 divides into both 9 and 12, and `b` divides into both `ab` and `b`.
It is often easier to identify one factor at a time: `6x^2 - 2x`:
`6x^2 - 2x`
`= 2(3x^2 - x)` - identifying 2 as a common factor
`= 2x(3x - 1)` - identifying `x` as a common factor.
Factorise `4ab - 20a`
The common factors are 4 and `a`; so the two factors act as multipliers outside the bracket.
Answer: `4a(b - 5)`
Factorise `15a^2b - 5ab`
`15a^2b - 5ab`
`= 5(3a^2b - ab)`
`= 5a(3ab - b)`
`= 5ab(3a - 1)`
Answer: 5ab(3a - 1)
See also Factors