If a + b = 2 and ab = 3, then find a^3 + b^3.
a + b = 2 square both sides
a^2 + 2ab + b^2 = 4 a^3 + b^3 =
a^2 + 2(3) + b^2 = 4 (a + b) ( a^2 - ab + b^2)
a^2 + b^2 + 6 = 4 (a + b) ( a^2 + b^2 - ab) =
a^2 + b^2 = -2 (2) ( -2 - 3) =
2 (-5) =
-10
