# Factorization

**Factorising expressions**

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)

Example 1

Factorise the following expression: 5*x* + 10

(5 and 10 has a common factor of 5)

Therefore:

(5*x* + 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.

For example:

Factorise the following expression: 5*a* + *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*.

5*a* + *ab* + 5 + *b *= 5*a* + 5 + *ab* + *b*

= 5(*a* + 1) + *b*(*a* + 1) (here the common factor is (*a* + 1) therefore)

(*a* + 1)(5 + *b*)