If (x+y)=17 and xy=9, then what is the value of x
3
+y
3
?

We can use the standard algebraic identity for x
3
+y
3
:

x
3
+y
3
=(x+y)
3
−3xy(x+y)
Substitute the given values into the formula:

x+y=17

xy=9

x
3
+y
3
=(17)
3
−3(9)(17)
x
3
+y
3
=4913−27×17
x
3
+y
3
=4913−459
x
3
+y
3
=4454