Factor polynomial $$ 8mu-10mv+12nu-15nv $$

$$ 8mu-10mv+12nu-15nv = (2m+3n)(4u-5v) $$

To factor $ 8mu-10mv+12nu-15nv $ we can use factoring by grouping.

Group $ \color{blue}{ 8mu }$ with $ \color{blue}{ -10mv }$ and $ \color{red}{ 12nu }$ with $ \color{red}{ -15nv }$ then factor each group.

$$ \begin{aligned} 8mu-10mv+12nu-15nv &= ( \color{blue}{ 8mu-10mv } ) + ( \color{red}{ 12nu-15nv }) = \\ &= \color{blue}{ 2m( 4u-5v )} + \color{red}{ 3n( 4u-5v ) } = \\ &= (2m+3n)(4u-5v) \end{aligned} $$

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