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, |

__QUADRATIC factorising.____ Part
1:__

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, |

__Grade A factorising__

It is much trickier to factorise expressions such as: To attempt this requires a trial and error approach, focusing
on the first and last term, The terms which multiply to get are and an To number which multiply to get 5 are 5 and 1 We can therefore list all the possibilities WE THEN SEE WHICH ONE EXPANDS TO GIVE THE REQUIRED EXPRESSION So, |

AN EVEN LONGER EXAMPLE!!! Factorise The terms which multiply to make are:
The terms which multiply to make are:
OR
WE COULD THEREFORE BEGIN TO LIST ALL THE POSSIBILITIES!!! We can see how expands to give |

WOW, that takes some effort.

The next skill is to use factorising to solve quadratic equations.

There will be another set of notes on this area!