Factorising (CIE IGCSE Maths: Core)

What is factorisation?

• A factorised expression is one written as the product (multiplication) of two, or more, terms (factors)
  • 3(x  + 2) is factorised
    • It is 3 × (x  + 2)
  • 3x  + 6  is not factorised
  • 3xy  is factorised
    • It is 3 × x  × y
  • Numbers can also be factorised
    • 12 = 2 x 2 x 3
• In algebra, factorisation is the reverse of expanding brackets
  
  • It's putting it into brackets, rather than removing brackets

How do I factorise two terms?

• To factorise 12x² + 18x  
  • Find the highest common factor of the number parts
    • 6
  • Find the highest common factor of the algebra parts
    • x
  • Multiply both to get the overall highest common factor
    • 6x
  • 12x² + 18x  is the same as 6x  × 2x  + 6x  × 3
    • Using the highest common factor
  • Take out the highest common factor
    • Write it outside a set of brackets
    • Put the remaining terms, 2x  + 3,  inside the brackets
  • This gives the answer
    • 6x (2x  + 3)
• To factorise an expression containing multiple variables, e.g. 2a³b - 4a²b²
  • Use the same approach as above
  • Find the highest common factor of the number parts
    • 2
  • Find the highest common factor of the algebra parts
    • a and b appear in both terms
    • The highest common factor of a³ and a² is a²
    • The highest common factor of b and b² is b
    • a²b
  • Multiply both to get the overall highest common factor
    • 2a²b
  • 2a³b - 4a²b²  is the same as 2a²b  × a  -  2a²b  × 2b
    • Using the highest common factor
  • Take out the highest common factor
    • Write it outside a set of brackets
    • Put the remaining terms, a - 2b,  inside the brackets
  • This gives the answer
    • 2a²b (a - 2b)