Question

Prove that ( a+b+c ) ³ -a³-b³-c³ = 3 ( a+ b ) ( b+ c ) (c+a)

Answer 1

(a+b+c)3=(a+b+c)2(a+b+c)

(a+b+c)3=a2(b+c)+b2(a+c)+c2(a+b)+2(ab+bc+ac)(a+b+c)

=a3+b3+c3+3a2(b+c)+3b2(a+c)+3c2(a+b)+6abc

(a+b+c)3 - a3-b3-c3 =a3+b3+c3+3(a+b)(b+c)(a+c)