Factorise: $x (x - 2) (x - 4) + 4 x - 8$ .....[2 marks]

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Solution

$x (x - 2) (x - 4) + 4 x - 8$

$= x (x - 2) (x - 4) + 4 (x - 2)$

$= (x - 2) [x (x - 4) + 4]$
$= (x - 2) (x^{2} - 4 x + 4)$ ........[1 mark]
$= (x - 2) [x^{2} - 2 \times x \times 2 + 2^{2}]$
$= (x - 2) (x - 2)^{2}$
$= (x - 2)^{3}$ ...........[1 mark]

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