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)#