Question 166349
Are you trying to factor {{{27x^3y^3-125}}}? 



{{{27x^3y^3-125}}} Start with the given expression



{{{(3xy)^3-(5)^3}}} Rewrite {{{27x^3y^3}}} as {{{(3xy)^3}}} and {{{125}}} as {{{(5)^3}}}



{{{A^3-B^3=(A-B)(A^2+AB+B^2)}}} Start with <a href="http://www.purplemath.com/modules/specfact2.htm">Difference of Cubes Formula</a>



{{{(3xy)^3-(5)^3=(3xy-5)((3xy)^2+(3xy)(5)+5^2)}}} Plug in {{{A=3xy}}} and {{{B=5}}}



{{{(3xy)^3-(5)^3=(3xy-5)(9x^2y^2+(3xy)(5)+25)}}} Square the values



{{{(3xy)^3-(5)^3=(3xy-5)(9x^2y^2+15xy+25)}}} Multiply



So {{{27x^3y^3-125}}} factors to {{{(3xy-5)(9x^2y^2+15xy+25)}}}.



So the only mistake you made was the sign of the middle term {{{15xy}}}