Factor polynomial $$ lm^{2}-mn^{2}-lm+n^{2} $$

$$ lm^{2}-mn^{2}-lm+n^{2} = (m-1)(lm-n^{2}) $$

To factor $ lm^2-mn^2-lm+n^2 $ we can use factoring by grouping.

Group $ \color{blue}{ lm^2 }$ with $ \color{blue}{ -mn^2 }$ and $ \color{red}{ -lm }$ with $ \color{red}{ n^2 }$ then factor each group.

$$ \begin{aligned} lm^2-mn^2-lm+n^2 &= ( \color{blue}{ lm^2-mn^2 } ) + ( \color{red}{ -lm+n^2 }) = \\ &= \color{blue}{ m( lm-n^2 )} \color{red}{ -1( lm-n^2 ) } = \\ &= (m-1)(lm-n^2) \end{aligned} $$

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