Factor polynomial $$ a^{2}b^{2}+2a^{2}b+3ab^{2}+6ab $$

$$ a^{2}b^{2}+2a^{2}b+3ab^{2}+6ab = ab(a+3)(b+2) $$

Step 1 :

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

$$ a^2b^2+2a^2b+3ab^2+6ab = ab ( ab+2a+3b+6 ) $$

Step 2 :

To factor $ ab+2a+3b+6 $ we can use factoring by grouping.

Group $ \color{blue}{ ab }$ with $ \color{blue}{ 2a }$ and $ \color{red}{ 3b }$ with $ \color{red}{ 6 }$ then factor each group.

$$ \begin{aligned} ab+2a+3b+6 &= ( \color{blue}{ ab+2a } ) + ( \color{red}{ 3b+6 }) = \\ &= \color{blue}{ a( b+2 )} + \color{red}{ 3( b+2 ) } = \\ &= (a+3)(b+2) \end{aligned} $$

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