### Factorisation

Factorise is the inverse of expand where you put the brackets back into the equation. You need to look for the highest common factor (HCF) of both terms.

Note: for a recap on expand refer to Expand Brackets − 1

Note: for a more detailed recap on expand refer to Expand Brackets − 2

Note: for a recap on HCF refer to HCF

#### Example 1. Factorise 6a + 30

#### Example 2. Factorise a + 3ab

#### Example 3. Factorise 4a + 20ab

#### Example 4. Factorise 14a + 63ab

6a + 30 | has the HCF of 6 | |

6a + 30 | = 6 × a + 6 × 5 | |

= 6 × (a + 5) | ||

= 6(a + 5) |

a + 3ab | has the HCF of a | |

a + 3ab | = a × 1 + a × 3b | |

= a × (1 + 3b) | ||

= a(1 + 3b) |

4a + 20ab | has the HCF of 4a | |

4a + 20ab | = 4a × 1 + 4a × 5b | |

= 4a × (1 + 5b) | ||

= 4a(1 + 5b) |

14a + 63ab | has the HCF of 7a | |

14a + 63ab | = 7a × 2 + 7a × 9b | |

= 7a × (2 + 9b) | ||

= 7a(2 + 9b) |

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