What is the value of $a^3 + b^3$ given that $a+b=10$ and $ab=17$?
I notice that $a^3 + b^3$ can be rewritten as $(a+b)(a^2 - ab + b^2)$ by using the sum of cubes formula. This might be helpful because I already know the value of $a+b$ and $ab$. So I substitute those values into the expression and get $(10)(a^2 - 17 + b^2)$. Now I need to find the value of $a^2 + b^2$. I recall that $(a+b)^2 = a^2 + 2ab + b^2$, so I can rearrange this equation to get $a^2 + b^2 = (a+b)^2 - 2ab$. Again, I substitute the known values of $a+b$ and $ab$ and get $a^2 + b^2 = (10)^2 - 2(17) = 100 - 34 = 66$. So I plug this into the expression for $a^3 + b^3$ and get $(10)(66 - 17) = (10)(49) = 490$. 