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

Jun 7, 2015

We see all the numbers can be divided by $\textcolor{b l u e}{4}$ so we know we can factor by $\textcolor{b l u e}{4}$ :

$= \textcolor{b l u e}{4} \left(2 {x}^{3} {y}^{2} - 3 {x}^{2} {y}^{3} + 5 {x}^{2} {y}^{2}\right)$

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)