Factor polynomial $$ 20y^{2}-5y^{2}z+4z-z^{2} $$

$$ 20y^{2}-5y^{2}z+4z-z^{2} = (5y^{2}+z)(4-z) $$

To factor $ 20y^2-5y^2z+4z-z^2 $ we can use factoring by grouping.

Group $ \color{blue}{ 20y^2 }$ with $ \color{blue}{ -5y^2z }$ and $ \color{red}{ 4z }$ with $ \color{red}{ -z^2 }$ then factor each group.

$$ \begin{aligned} 20y^2-5y^2z+4z-z^2 &= ( \color{blue}{ 20y^2-5y^2z } ) + ( \color{red}{ 4z-z^2 }) = \\ &= \color{blue}{ 5y^2( 4-z )} + \color{red}{ z( 4-z ) } = \\ &= (5y^2+z)(4-z) \end{aligned} $$

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