Factor polynomial $$ 6a^{2}+6ab-12a-12b $$

$$ 6a^{2}+6ab-12a-12b = 6(a-2)(a+b) $$

Step 1 :

Factor out common factor $ \color{blue}{ 6 } $:

$$ 6a^2+6ab-12a-12b = 6 ( a^2+ab-2a-2b ) $$

Step 2 :

To factor $ a^2+ab-2a-2b $ we can use factoring by grouping.

Group $ \color{blue}{ a^2 }$ with $ \color{blue}{ ab }$ and $ \color{red}{ -2a }$ with $ \color{red}{ -2b }$ then factor each group.

$$ \begin{aligned} a^2+ab-2a-2b &= ( \color{blue}{ a^2+ab } ) + ( \color{red}{ -2a-2b }) = \\ &= \color{blue}{ a( a+b )} \color{red}{ -2( a+b ) } = \\ &= (a-2)(a+b) \end{aligned} $$

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