Question

(b+c)^3 (b-c)^3 + (c-b)^3 (c+b)^3 + (a-b)^3 (a+b)^3​

Answer 1

(b+c)³ (b-c)³ + (c-b)³ (c+b)³ + (a-b)³ (a+b)³

Identity used :

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³-3a²b-3ab²+b³

Using above identity, we get :

(b³+c³)(b³+c³) + (c³+b³)(c³+b³) + (a³+b³)(a³+b³)

b⁶+2b³c³+c⁶ + c⁶+2b³c³+b⁶ + a⁶+2a³b³+b⁶

3b⁶ + 2c⁶ + a⁶ + 4b³c³ + 2a³b³