Factor polynomial $$ 6am+10an-3bm-5bn $$

$$ 6am+10an-3bm-5bn = (2a-b)(3m+5n) $$

To factor $ 6am+10an-3bm-5bn $ we can use factoring by grouping.

Group $ \color{blue}{ 6am }$ with $ \color{blue}{ 10an }$ and $ \color{red}{ -3bm }$ with $ \color{red}{ -5bn }$ then factor each group.

$$ \begin{aligned} 6am+10an-3bm-5bn &= ( \color{blue}{ 6am+10an } ) + ( \color{red}{ -3bm-5bn }) = \\ &= \color{blue}{ 2a( 3m+5n )} \color{red}{ -b( 3m+5n ) } = \\ &= (2a-b)(3m+5n) \end{aligned} $$

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