Question 1020225
 {{{x^4y^5+x^5y^4 = 810 }}}==>{{{x^3y^3(x^2y+xy^2) = 810}}} after factoring {{{x^3y^3}}} and changing the order of the terms.

==> {{{x^3y^3(3x^2y+3xy^2) = 2430}}}     (Equation A)

after multiplying both sides by 3.

Similarly, factor out {{{x^3y^3}}} from the 2nd equation {{{x^6y^3+x^3y^6 = 945}}}:

{{{x^3y^3(x^3 + y^3) = 945}}}             (Equation B)

Add corresponding sides of Eqn. A and Eqn. B, to get

{{{x^3y^3(x^3 + 3x^2y+3xy^2+ y^3) = 3375}}} 
==>{{{x^3y^3(x+y)^3 = 3375}}}
==> xy(x+y) = 15,                         (Equation C)
after taking cube roots of both sides.

Now the first equation  {{{x^4y^5+x^5y^4 = 810 }}} is the same as 
{{{x^4y^4(x+y) = 810}}}                 (Equation D)
Dividing Eqn.D by Eqn.C, we get

{{{x^3y^3 = 810/15 =54}}}
Hence, {{{ (xy)^3=54}}}               (Equation E)   

Putting {{{x^3y^3 = 54}}} into Eqn.B, we get
{{{54(x^3+y^3) = 945}}} ==> {{{x^3+y^3 = 35/2}}}, or  
{{{2x^3+2y^3 = 35}}}                    (Equation F)

Finally, combining Equations E and F, we get 

{{{2x^3+(xy)^3+2y^3 = 35+54 = highlight(89)}}}.