Question

`2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3 sqrt6abc`

Answer 1

`= (sqrt2a)^3+ (sqrt3b)^3 + c^3 - 3 xx sqrt2a xx sqrt3b xx c`

`=(sqrt2a + sqrt3b + c)((sqrt2a)^2 + (sqrt3b)^2 + c^2 - (sqrt2a)(sqrt3) - (sqrt3b)c - (sqrt2a)c)`

`= (sqrt2 + sqrt3b + c)(2a^2 + 3b^2 + c^2 - sqrt6ab - sqrt3bc - sqrt2ac)`

`∴ 2sqrt2a^3 + 3sqrt3b^3 + c^3 - 3sqrt6abc = (sqrt2a + sqrt3b + c)(2a^2 + 3b^2 + c^2 - sqrt6ab - sqrt3bc - sqrt2ac)`