Factor polynomial $$ 6x^{2}+4xy+15x+10y $$

$$ 6x^{2}+4xy+15x+10y = (2x+5)(3x+2y) $$

To factor $ 6x^2+4xy+15x+10y $ we can use factoring by grouping.

Group $ \color{blue}{ 6x^2 }$ with $ \color{blue}{ 4xy }$ and $ \color{red}{ 15x }$ with $ \color{red}{ 10y }$ then factor each group.

$$ \begin{aligned} 6x^2+4xy+15x+10y &= ( \color{blue}{ 6x^2+4xy } ) + ( \color{red}{ 15x+10y }) = \\ &= \color{blue}{ 2x( 3x+2y )} + \color{red}{ 5( 3x+2y ) } = \\ &= (2x+5)(3x+2y) \end{aligned} $$

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