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]3=(a+b)3+3(a+b)2c+3(a+b)c2+c3

=>(a+b+c)3=(a3+3a2b+3ab2+b3)+3(a2+2ab+b2)c+3(a+b)c2+c3

=>(a+b+c)3=a3+b3+c3+3a2b+3a2c+3ab2+3b2c+3ac2+3bc2+6abc

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

hence proved