To factor $ 44fg+63f-44g-63 $ we can use factoring by grouping.

Group $ \color{blue}{ 44fg }$ with $ \color{blue}{ 63f }$ and $ \color{red}{ -44g }$ with $ \color{red}{ -63 }$ then factor each group.

$$ \begin{aligned} 44fg+63f-44g-63 &= ( \color{blue}{ 44fg+63f } ) + ( \color{red}{ -44g-63 }) = \\ &= \color{blue}{ f( 44g+63 )} \color{red}{ -1( 44g+63 ) } = \\ &= (f-1)(44g+63) \end{aligned} $$

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