Question

hey anyone can solve my problem pleaseeeee

Answer 1

Given :

(a + b + c)^3 - a^3 - b^3 - c^3:  - -------- (1)

[(a + b) + c)^3 = (a + b)^3 + 3(a + b)^2c + 3(a + b)c^2 + c^3
  
           = a^3 + 3a^2b + 3ab^2 + b^3 + 3(a^2 + 2ab + b^2)c + 3(a + b)c^2 + c^3

           = a^3 + 3a^2b + 3ab^2 + b^3 + 3a^2c + 6abc + 3b^2c + 3ac^2 + 3bc^2 + c^3   ----- (2)


Now,


Substiute (2) in (1), we get

= > a^3 + 3a^2b + 3ab^2 + b^3 + 3a^2c + 6abc + 3b^2c + 3ac^2 + 3bc^2 + c^3 - a^3 - b^3 - c^3

= > 3a^2b + 3ab^2 + 3a^2c + 6abc + 3b^2c + 3ac^2 + 3bc^2 

= > 3(a^2b + ab^2 + a^2c + 2abc + b^2c + ac^2 + bc^2)

= > 3(ab + ac + b^2 + bc)(c + a)

= > 3(a + b)(b + c)(c + a).


Hope this helps!