Given $x+y$ and $x\cdot y$, what is $x^3+ y^3$ ? I have been looking at an assortment of high school number sense tests and I noticed a reoccurring problem that states what x+y is and what $x\cdot y$ is then asks for $x^3+ y^3$. I want to know how to work these problems. I have a couple of examples.
$x+y=5$ and $x\cdot y=1$, then $x^3+y^3=?$ [key says 110]
$x+y=-1$ and $x\cdot y=2$, then $x^3+y^3=?$ [key says 5]
$x-y=-1$ and $x\cdot y=2$, then $x^3 -y^3=?$ [key says -7]
$x+y=\frac{1}{3}$ and $x\cdot y=\frac{1}{9}$, then $x^3+y^3=?$ $\left[-\dfrac{2}{27}\right]$

Its simple. Use the identity 
${x^3 + y^3 =(x+y)(x^2 +y^2 -xy) }$
In the above identity;
make modifications and bring it to this form :
${x^3+y^3 = (x+y)((x+y)^2 -3xy) }$
Now putting the values of ${x+y}$ and ${xy}$ in the above equations, you should get the correct answer.
:)
