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

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

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Answer 1 · 2015-06-07T08:43:33

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

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

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

$2 x^{3} y^{2} = 2 \cdot x \cdot x^{2} y^{2} = 2 x \cdot (x^{2} y^{2})$ $2x^3y^2=2*x*x^2y^2=color(red)(2x)*color(purple)((x^2y^2)$

$- 3 x^{2} y^{3} = - 3 \cdot y \cdot x^{2} y^{2} = - 3 y \cdot (x^{2} y^{2})$ $-3x^2y^3=-3*y*x^2y^2=color(red)(-3y)*color(purple)((x^2y^2)$

$5 x^{2} y^{2} = 5 \cdot (x^{2} y^{2})$ $5x^2y^2=color(red)5*color(purple)((x^2y^2)$

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

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

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