Factor polynomial $$ 5xy^{2}+5xy-y^{2}-y $$

$$ 5xy^{2}+5xy-y^{2}-y = y(5x-1)(y+1) $$

Step 1 :

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

$$ 5xy^2+5xy-y^2-y = y ( 5xy+5x-y-1 ) $$

Step 2 :

To factor $ 5xy+5x-y-1 $ we can use factoring by grouping.

Group $ \color{blue}{ 5xy }$ with $ \color{blue}{ 5x }$ and $ \color{red}{ -y }$ with $ \color{red}{ -1 }$ then factor each group.

$$ \begin{aligned} 5xy+5x-y-1 &= ( \color{blue}{ 5xy+5x } ) + ( \color{red}{ -y-1 }) = \\ &= \color{blue}{ 5x( y+1 )} \color{red}{ -1( y+1 ) } = \\ &= (5x-1)(y+1) \end{aligned} $$

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