Question

a+b+c whole cube formula​

Answer 1

Answer:

Step-by-step explanation:

The Formula is given below :

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

Explanation :

Let us just start with 

(a+b+c)² = a² +b² + c²+2ab+2bc+2ca

=a² +b² + c²+2(ab+bc+ca)

now:

(a+b+c)² (a+b+c)=(a + b + c)³=[a² +b² + c²+2(ab+bc+ca)](a+b+c)

=a²[a+b+c] +b²[a+b+c]+c²[a+b+c] +2[(ab+bc+ca)[a+b+c]]

=a³+a²b+a²c + b²a+b³+b²c + c²a +c²b +c³ + 2ab[a+b+c] +2bc(a+b+c)

+2ca(a+b+c)

=a³+a²b+a²c + b²a+b³+b²c + c²a +c²b +c³ +2a²b+2ab²+2abc +2abc+2b²c +2bc² +2a²c +2abc +2a²c

=a³+b³+c³+6abc +a²b+2a²b+a²c + b²a+b²c+2ab² +c²a+c²b+2c²b

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

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

on further simplifying, we get

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