Common Factors

Common Factors

Factorising based on common factors relies on there being factors common to all the terms.

For example, \(2x - 6{x}^{2}\) can be factorised as follows:

\[2x - 6{x}^{2} = 2x(1 - 3x)\]

And \(2(x - 1) - a(x - 1)\) can be factorised as follows:

\[(x - 1)(2 - a)\]

The following video shows an example of factorising by taking out a common factor.

Example

Question

Factorise: \[5(a - 2) - b(2 - a)\]

Use a “switch around” strategy to find the common factor.

Notice that \(2-a=-(a-2)\)

\begin{align*} 5(a - 2)-b(2 - a) & = 5(a - 2) - [-b(a - 2)] \\ & =5(a - 2) + b(a - 2) \\ & =(a - 2)(5 + b) \end{align*}

This lesson is part of:

Algebraic Expressions Overview

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