It is important to understand the distinction between expanding and factorising.

These concepts occur across a range of Mathematical Ideas

Factorising – lots of examples

Read through each one carefully – make sure you understand each one

Factorising is about PUTTING an expression BACK INTO BRACKETS.

To understand factorising requires you to understand EXPANDING BRACKETS

 Suppose you are asked to factorise: ,   We need to find the HIGHEST COMMON FACTOR (HCF) of 5 and 10.   The highest number which goes in to 5 and 10 is 5   So, Factorise,   The HCF of 12 and 18 is 6   So Factorise,   The HCF of 24 and 8 is 8  [ignore the minus sign for the moment   So, Factorise,   This is more subtle, there is a common factor of   So,      [think carefully, Factorise,   There are two parts to this   The HCF of 4 and 12 is 4   However, there is also a common factor of   So,

 If you are asked to factorise , we need to focus on the +6.   The KEY QUESTION here is: what two numbers MULTIPLY to make 6 and ADD to make 5   The numbers are   So, If you are asked to factorise , we need to focus on the +16.   The KEY QUESTION here is: what two numbers MULTIPLY to make 16 and ADD to make 10   The numbers are   So, Factorise,   So, Factorise,   Be careful, we need two numbers which multiply to make   So, Factorise,   So, SPECIAL CASE: THE DIFFERENCE OF TWO SQUARES   Factorise,   NOTICE HOW 25 and  are both square numbers,  and   So, Factorise, So, Factorise, So,