The term factorising an expression is to do the opposite of expanding it. Therefore when expanding an expression, the brackets are removed and when factorising, the expression is written with brackets.
An example of Factorising the expression is as follows:
a(b + c) → ab + ac (expanding or multiplying out)
ab + ac → a(b + c) (factorising)
Factorise the following expression: 5x + 10
(5 and 10 has a common factor of 5)
(5x + 10) ÷ 5 = x + 2 (this means that 5 can be written outside the brackets)
=5(x + 2)
Factorization by pairing
Factorisation takes factoring another level by taking expressions containing four terms and regrouping them into pairs which share a common factor.
Factorise the following expression: 5a + ab + 5 + b
Note: there are two terms which share a common factor of 5 and two remaining terms which share a common factor of b.
5a + ab + 5 + b = 5a + 5 + ab + b
= 5(a + 1) + b(a + 1) (here the common factor is (a + 1) therefore)
(a + 1)(5 + b)