∵a+b=1
∴a³＋b³＋3ab²＋3a²b
＝﹙a³＋b³﹚＋﹙3ab²＋3a²b﹚
＝=(a+b)(a²-ab+b²)+3ab(a+b)
=(a+b)(a²-ab+b²+3ab)
=(a+b)(a²+2ab+b²)
=(a+b)³
=1³
=1