Factorising Out Terms (Cambridge (CIE) IGCSE International Maths)

Basic Factorising

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)