Formulas where Subject Appears Twice (Cambridge (CIE) IGCSE International Maths)

Subject Appears Twice

How do I rearrange formulae where the subject appears twice?  

• If the subject appears twice, you will need to factorise at some point

  • E.g. When making the subject of

  • Factorise out on the left to get

    • Notice that the subject now only appears once!

  • Then divide both sides by to get

• If the subject appears twice, and any of these are inside a set of brackets, you will need to expand these brackets first

  • E.g. When making the subject of

  • Expand the bracket first to

  • Keep the terms on one side

  • can then be made the subject using factorising as above

• If the subject appears on two sides of a formula, you will need to bring those terms to the same side before you can factorise

  • E.g. When making the subject of

  • Add to both sides first to form

  • can then be made the subject using factorising as above

How do I factorise powers of a subject? 

• If the subject appears twice, and both have the same power, you will need to collect these terms together before applying their inverse

  • E.g. When making the subject of

  • Add to both sides first to form

  • can then be factorised out to give

    • Now take plus-or-minus square roots

    • 

• Be careful when square rooting, or cube rooting etc

  • E.g. To make the subject of

    • The whole right hand side must be cube rooted

    • 

    • This cannot be simplified further

    • The right hand side is not equal to , (this is a common error)