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General algebra

Factorisation

  • The reverse process to expanding is called factorisation. In this case we are given an expression which is a sum of terms and we convert it to a product of two or more terms.
  • Expressions may be factorised by removing factors common to two or more terms and then by grouping and if necessary regrouping.
  • For example: \(
    \newcommand{\eqncomment}[2]{\small{\text{ #2}} } 
    \newcommand{\ceqns}{\begin{array}{rcll}}
    \newcommand{\ceqne}{\end{array}}
    \)
    \[
    \ceqns
    && 3x+3x^2 \\
    &=& 3\times x+2x\times x & \eqncomment{0.4}{where \(x\) is the common factor} \\
    &=& x(3+2x)
    \ceqne
    \]
  • Another example of factorising:
\begin{eqnarray}
2x^{3} +4x^{2}+6x = 2x(x^{2}+2x+3)
\end{eqnarray}
where \(2x\) is the common factor.

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