Factor polynomial $$ x^{3}y^{3}+2x^{3}+5x^{2}y^{3}+10x^{2} $$

$$ x^{3}y^{3}+2x^{3}+5x^{2}y^{3}+10x^{2} = x^{2}(x+5)(y^{3}+2) $$

Step 1 :

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

$$ x^3y^3+2x^3+5x^2y^3+10x^2 = x^2 ( xy^3+2x+5y^3+10 ) $$

Step 2 :

To factor $ xy^3+2x+5y^3+10 $ we can use factoring by grouping.

Group $ \color{blue}{ xy^3 }$ with $ \color{blue}{ 2x }$ and $ \color{red}{ 5y^3 }$ with $ \color{red}{ 10 }$ then factor each group.

$$ \begin{aligned} xy^3+2x+5y^3+10 &= ( \color{blue}{ xy^3+2x } ) + ( \color{red}{ 5y^3+10 }) = \\ &= \color{blue}{ x( y^3+2 )} + \color{red}{ 5( y^3+2 ) } = \\ &= (x+5)(y^3+2) \end{aligned} $$

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