How do you factor $8x^3y^2 - 12x^2y^3 + 20x^2y^2$ ?

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Answer 1 · 2015-06-07T08:43:33

We see all the numbers can be divided by $color(blue)4$ so we know we can factor by $color(blue)4$ :

$=color(blue)4(2x^3y^2-3x^2y^3+5x^2y^2)$

We are now going to look at every member in the parenthesis :

$2x^3y^2=2*x*x^2y^2=color(red)(2x)*color(purple)((x^2y^2)$

$-3x^2y^3=-3*y*x^2y^2=color(red)(-3y)*color(purple)((x^2y^2)$

$5x^2y^2=color(red)5*color(purple)((x^2y^2)$

Thus : $color(blue)4(2x^3y^2-3x^2y^3+5x^2y^2)=color(blue)4color(purple)((x^2y^2)color(red)((2x-3y+5)$

How do you factor 8x^3y^2 - 12x^2y^3 + 20x^2y^2 8x^3y^2 - 12x^2y^3 + 20x^2y^2?