Given that \(a+b=5\) and \(a^2+b^2=15\), find \(a^3+b^3\).
\(a^3 + b^3 = (a+b)(a^2 -ab +b^2)=\\ (a+b)^2 = a^2 + b^2 + 2ab=15+2ab=25\\ 2ab=10\\ ab=5\\ a^3+b^3=5(15-5)=50\)
That was much simpler than what I was thinking
