Factorising General Quadratics and Differences of Squares

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Any expression of the formcannot be factorised as with simple quadratics, by finding factors of c. Instead there is a slightly more complicated procedure, best illustrated by an example:

Factorise

  1. Take out any common factor. Every term in the above expression has a factor 3, so we may write the expression as
  2. Multiply the coefficient ofby the constant term:Find the two factors of this product which add to give the coefficient ofwhich in this case is -1.
  3. Rewrite the term in brackets using these two factors:
  4. Take out common factors for each pair:
  5. Factorise completely:

Example

Factorise

  1. Take out common factors:
  2. Multiply the coefficient ofby the constant term:Find the two factors of this product which add to give the coefficient ofwhich in this case is -7: -1 and -6.
  3. Rewrite the term in brackets using these two factors:
  4. Take out common factors for each pair:
  5. Factorise completely:

Differences of Squares

Any expression of the formcan be factorised almost instantly:

Example:

Example:

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