Question 88739
{{{x^5y^3-9x^4y^2+20x^3y}}}


{{{x^3y(x^2y^2-9xy+20)}}} Factor out the GCF {{{x^3y}}}


Now what 2 numbers multiply to 20 and add to -9? These 2 numbers are -4 and -5


So these 2 numbers are placed into the blank expression


{{{(xy+a)(xy+b)}}} where a=-4 and b=-5


{{{x^3y(xy-4)(xy-5)}}} Plug in a=-4 and b=-5


Notice how {{{(xy-4)(xy-5)}}} foils back to {{{x^2y^2-9xy+20}}} so our answer is  verified 


So {{{x^5y^3-9x^4y^2+20x^3y}}} factors to {{{x^3y(xy-4)(xy-5)}}}