How do you factor: $3 y - 6 x + 4 x y - 2 y^{2}$ $3y - 6x + 4xy - 2y^2$ ?

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How do you factor: $3 y - 6 x + 4 x y - 2 y^{2}$ $3y - 6x + 4xy - 2y^2$ ?

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Answer 1 · 2016-08-29T17:35:35

$(y - 2 x) (3 - 2 y)$ $(y-2x)(3-2y)$

Explanation:

Group the terms in 'pairs'

That is $[3 y - 6 x] + [4 x y - 2 y^{2}]$ $[3y-6x]+[4xy-2y^2]$

now factorise each 'pair' by taking out a $common factor$ $color(blue)"common factor"$

$\Rightarrow 3 (y - 2 x) - 2 y (y - 2 x)$ $rArrcolor(red)(3)(y-2x)color(red)(-2y)(y-2x)$

We now have a $common factor$ $color(blue)"common factor"$ of (y - 2x)

$\Rightarrow (y - 2 x) (3 - 2 y)$ $rArr(y-2x)(color(red)(3-2y))$

$\Rightarrow 3 y - 6 x + 4 x y - 2 y^{2} = (y - 2 x) (3 - 2 y)$ $rArr3y-6x+4xy-2y^2=(y-2x)(3-2y)$

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How do you factor: $3 y - 6 x + 4 x y - 2 y^{2}$ $3y - 6x + 4xy - 2y^2$ ?

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