Factor polynomial $$ 4st^{2}+2st-2t^{2}-t $$

$$ 4st^{2}+2st-2t^{2}-t = t(2s-1)(2t+1) $$

Step 1 :

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

$$ 4st^2+2st-2t^2-t = t ( 4st+2s-2t-1 ) $$

Step 2 :

To factor $ 4st+2s-2t-1 $ we can use factoring by grouping.

Group $ \color{blue}{ 4st }$ with $ \color{blue}{ 2s }$ and $ \color{red}{ -2t }$ with $ \color{red}{ -1 }$ then factor each group.

$$ \begin{aligned} 4st+2s-2t-1 &= ( \color{blue}{ 4st+2s } ) + ( \color{red}{ -2t-1 }) = \\ &= \color{blue}{ 2s( 2t+1 )} \color{red}{ -1( 2t+1 ) } = \\ &= (2s-1)(2t+1) \end{aligned} $$

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