Factor polynomial $$ 2mn+8n+12m+48 $$

$$ 2mn+8n+12m+48 = 2(n+6)(m+4) $$

Step 1 :

Factor out common factor $ \color{blue}{ 2 } $:

$$ 2mn+8n+12m+48 = 2 ( mn+4n+6m+24 ) $$

Step 2 :

To factor $ mn+4n+6m+24 $ we can use factoring by grouping.

Group $ \color{blue}{ mn }$ with $ \color{blue}{ 4n }$ and $ \color{red}{ 6m }$ with $ \color{red}{ 24 }$ then factor each group.

$$ \begin{aligned} mn+4n+6m+24 &= ( \color{blue}{ mn+4n } ) + ( \color{red}{ 6m+24 }) = \\ &= \color{blue}{ n( m+4 )} + \color{red}{ 6( m+4 ) } = \\ &= (n+6)(m+4) \end{aligned} $$

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