If $x+y=9$ and $xy=10$, what is the value of $x^3+y^3$?
I know that $(x+y)^3=x^3+y^3+3xy(x+y)$, so I can use that to eliminate the cubic terms. If I plug in $x+y=9$ and $xy=10$, I get $(9)^3=x^3+y^3+3(10)(9)$. Simplifying, I get $729=x^3+y^3+270$. Subtracting 270 from both sides, I get $x^3+y^3=459$.

