Question:

Factorize: \[ x(x-2)(x-4)+4x-8 \]

Solution:

\[ x(x-2)(x-4)+4x-8 \]

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

\[ =(x-2)\{x(x-4)+4\} \]

\[ =(x-2)(x^2-4x+4) \]

\[ =(x-2)(x-2)^2 \]

\[ =(x-2)^3 \]

\[ \boxed{(x-2)^3} \]

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