Question

Prove that :
(a + b + c)^3 - a^3 - b^3 - c^3 = 3(a + b)(b+c)(c+a)​

Answer 1

Answer:

answer is one.

hope it help

Answer 2

Question:

Prove that :

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

Answer:

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

Left hand side:

[ (a+b+c)³-a³-b³-c³ ]

= [ (a+b+c)³-a³ ] - (b³+c³)  

= (a + b + c - a) [ (a + b + c)^2 + a^2 + a(a + b + c) - [(b+c) (b^2 + c^2 - bc)]

[we know that (a^3 + b^3) = (a+b) (a² + b² - ab) and (a^3 - b^3) = (a-b) (a² + b² + ab) ]

= (b+c) (a² + b² + c² + 2ab + 2bc + 2ca + a² + a² + ab + ac) - (b+c)( c² + b² - bc)

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

= 3(b+c) a(a+b) + c(a+b)  

= 3(a + b) (b+c) (c+a) (RHS proved)