Step 1 :

Factor out common factor $ \color{blue}{ b } $:

$$ 2a^3b-8a^2b+ab-4b = b ( 2a^3-8a^2+a-4 ) $$

Step 2 :

To factor $ 2a^3-8a^2+a-4 $ we can use factoring by grouping.

Group $ \color{blue}{ 2a^3 }$ with $ \color{blue}{ -8a^2 }$ and $ \color{red}{ a }$ with $ \color{red}{ -4 }$ then factor each group.

$$ \begin{aligned} 2a^3-8a^2+a-4 &= ( \color{blue}{ 2a^3-8a^2 } ) + ( \color{red}{ a-4 }) = \\ &= \color{blue}{ 2a^2( a-4 )} + \color{red}{ 1( a-4 ) } = \\ &= (2a^2+1)(a-4) \end{aligned} $$

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