`(a+b-c)^3`
` = [ (a+b) - c]^3`
`= (a+b)^3 - 3 . (a+b)^2 . c + 3 . (a+b) . c^2 - c^3`
` = (a^3 + 3a^2b + 3ab^2 + b^3) - 3c(a^2 + 2ab+b^2) + 3c^2 (a+b) - c^3`
` = a^3 + 3a^2b + 3ab^2 + b^3 - 3a^2c - 6abc - 3b^2c + 3ac^2 + 3bc^2 - c^3`
``
`(a+c - b)^3`
` = [ (a+c) - b]^3`
` = (a+c)^3 - 3 . (a+c)^2 . b + 3 . (a+c) . b^2 - b^3`
` = (a^3 + 3a^2c + 3ac^2 + c^3) - 3b (a^2 + 2ac + c^2) + 3b^2 (a+c) - b^3`
` = a^3 + 3a^2c + 3ac^2 + c^3 - 3a^2b - 6abc - 3c^2b + 3ab^2 + 3cb^2 - b^3`
``
`(b+c-a)^3`
` = [ (b+c) - a]^3`
` = (b+c)^3 - 3 . (b+c)^2 . a + 3 . (b+c) . a^2 - a^3`
` = (b^3 + 3b^2c + 3bc^2 + c^3) - 3a (b^2 + 2bc + c^2) + 3a^2 (b+c) - a^3`
` = b^3 + 3b^2c + 3bc^2 + c^3 - 3ab^2 - 6abc - 3ac^2 + 3a^2b + 3a^2c - a^3`