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Maths

Quadratic theory

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Factors

Factorising is the inverse of multiplying out the brackets. It's the process of taking a string of terms and regrouping them as expressions mulitplied together. You should remember from Intermediate 2 that there are three types of factors:

  • common factors

    2x^2 + 6xy = 2x(x + 3y)

    6p^2 q - 15pq^2 = 3pq(2p - 5q)

  • difference of two squares

    81 - 16x^2 = (9 - 4x)(9 + 4x)

    25x^2 - 49y^2 = (5x - 7y)(5x + 7y)

  • trinomials

    6x^2 - x - 2 = (2x + 1)(3x - 2)

    10x^2 + 19x - 15 = (2x + 5)(5x - 3)

These factors can be also applied to trigonometric expressions, that is, expressions involving involving sin x, cos x and tan x. For example:

\sin ^2 x - \cos ^2 x = (\sin x - \cos x)(\sin x + \cos x)

Remember that you can multiply out the brackets to check that you've not altered the original expression.

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Back to Algebra index

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GCSE Bitesize

GCSE Bitesize - Maths

Have you got the x-factor? Check out your factorising skills in this useful gsce bitesize activity.

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LTS - Mathematics

Download some of LTS'mathematic resources, have a look at the Sunday Herald's Exam Guide or brush up on your study skills.

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