Chứng minh rằng: (a + b + c)^3 = a^3 + b^3 + c^3 + 3(a + b).(b + c).(c + a).

(a+b+c)³

=(a+b)³+3(a+b)².c+3.(a+b).c²+c³

=a³+3a²b+3ab²+b³+3(a+b)².c+3.(a+b).c²+c³

=a³+b³+c³+[3a²b+3ab²+3(a+b)².c+3.(a+b).c²]

=a³+b³+c³+[3ab(a+b)+3(a+b)²c+3(a+b)c²]

=a³+b³+c³+3(a+b)[ab+(a+b)c+c²]

=a³+b³+c³+3(a+b)(ab+ac+bc+c²)

=a³+b³+c³+3(a+b)[a.(b+c)+c.(b+c)]

=a³+b³+c³+3(a+b)(b+c)(a+c).