`a) A = (a + b)^3 + (a - b)^3`

`= [(a + b) + (a - b)][(a + b)^2 - (a + b)(a - b) + (a - b)^2]`

`= [a + b + a - b][a^2 + 2ab + b^2 - a (a - b) - b (a - b) + a^2 - 2ab + b^2]`

`= 2a (a^2 + 2ab + b^2 - a^2 + ab - ab + b^2 + a^2- 2ab + b^2]`

`= 2a [(a^2 - a^2 + a^2) + (b^2 + b^2 + b^2) + (2ab + ab - ab - 2ab)]`

`= 2a (a^2 + 3b^2)`

`b) B = (x - z)^3 - 3 (z - x)^2 (a + b) + 3 (x - z)(a + b)^2 - (a + b)^3`

`= [(x - z) - ( a + b)]^3`

`= (x - z - a - b)^3`

`c) C = 6(c - d) (c+d)^2 + 12 (c - d)^2 (c+d) + (c+d)^3 + 8 (c - d)^3`

`= (c + d)^3 + 6 (c + d)^2 (c-d) + 12 (c-d)^2 (c+d) + 8 (c - d)^3`

`= (c + d)^3 + 3 (c + d)^2 2 . (c-d) + 3. 2^2 (c-d)^2 (c+d) + [2 (c - d)]^3`

`= [c + d + 2 (c - d)]^3`

`= (c + d + 2c - 2d)^3`

`= (3c - d)^3`