Factor polynomial $$ 18x^{2}y-24x^{2}-27y+36 $$

$$ 18x^{2}y-24x^{2}-27y+36 = 3(2x^{2}-3)(3y-4) $$

Step 1 :

Factor out common factor $ \color{blue}{ 3 } $:

$$ 18x^2y-24x^2-27y+36 = 3 ( 6x^2y-8x^2-9y+12 ) $$

Step 2 :

To factor $ 6x^2y-8x^2-9y+12 $ we can use factoring by grouping.

Group $ \color{blue}{ 6x^2y }$ with $ \color{blue}{ -8x^2 }$ and $ \color{red}{ -9y }$ with $ \color{red}{ 12 }$ then factor each group.

$$ \begin{aligned} 6x^2y-8x^2-9y+12 &= ( \color{blue}{ 6x^2y-8x^2 } ) + ( \color{red}{ -9y+12 }) = \\ &= \color{blue}{ 2x^2( 3y-4 )} \color{red}{ -3( 3y-4 ) } = \\ &= (2x^2-3)(3y-4) \end{aligned} $$

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