Question 103908
{{{8x^3y^2 - 18xy^4}}} Start with the given expression



{{{2xy^2(4x^2 - 9y^2)}}} Factor out the GCF {{{2xy^2}}}



Now lets factor {{{4x^2 - 9y^2}}}



Let a=2x and b=3y


Notice we get 


{{{4x^2 - 9y^2=(2x)^2 - (3y)^2=a^2-b^2}}}


So let's use the difference of squares to factor (remember the difference of squares formula is {{{a^2-b^2=(a+b)(a-b)}}}



{{{(2x)^2 - (3y)^2=(2x+3y)(2x-3y)}}}



{{{2xy^2(2x+3y)(2x-3y)}}} Now replace {{{4x^2 - 9y^2}}} in {{{2xy^2(4x^2 - 9y^2)}}}  with {{{(2x+3y)(2x-3y)}}}



So {{{8x^3y^2 - 18xy^4}}} factors to {{{2xy^2(2x+3y)(2x-3y)}}}