Factorize:$x(x – 2) (x – 4) + 4x – 8$

Given :

$x(x – 2) (x – 4) + 4x – 8$

To do :

We have to factorize the given expression.

Solution :

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

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

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

$= (x - 2) [(x)^2 - 2 \times x \times 2 + (2)^2]$

$= (x - 2) (x - 2)^2$

$= (x - 2)^3$

Hence, $x(x - 2) (x - 4) + 4x - 8 = (x - 2)^3$.

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Updated on: 10-Oct-2022

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