+218 Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$
+267 We can use the fact (a+b)3=a3+3a2b+3ab2+b3 to our advantage.
Expanding the left side, we get
\begin{align*} (a + b)^3 &= a^3 + 3a^2 b + 3ab^2 + b^3 \ &= a^3 + b^3 + 3ab (a + b). \end{align*}
Since we are given that a+b=4, this becomes a^3 + b^3 + 3ab(4) = 6.
Then a^3 + b^3 = −10.
