If $a+b=69$ and $a^2+b^2=2525$, find $a^3+b^3=?$
a + b = 69 square both sides
a^2 + 2ab + b^2 = 4761
a^2 + b^2 + 2ab = 4761
2525 + 2ab = 4761
2525 - 4761 = - 2ab
-2236 = -2ab
1118 = ab
a^3 + b^3 = ( a + b ) ( a^2 - ab + b^2) = (a + b) (a^2 + b^2 - ab) =
(69) ( 2525 - 1118)
(69) ( 1407) = 97083
