Find the expansion of `(3x^2-2a x+3a^2)^3` using binomial theorem.

Explanation

`(a-b)^{3}=a^{3}-3 a^{2} b+3 a b^{2}-b^{3}`

`(3 x^{2}-2 a x+3 a^{2})^{3}=[3 x^{2}-a(2 x-3 a)]^{3}`

`=(3 x^{2})^{3}-3(3 x^{2})^{2} a(2 x-30)+3 times 3 x^{2} a^{2}(2 x-3 a)^{2}-a^{3}(2 x-3 a)^{3}`

`=27 x^{6}-27 x^{4} a(2 x-3 a)+a x^{2} a^{2}(4 x^{2}-12 a x+9 a^{2})-a^{3}(8 x^{3}-3 times 4 times x^{2} times 3 a+3 times`

`4 times x^{2} times 3 a+3 times 2 x times 9 a^{2}-27+a^{3})`

`=27 x^{6}-54 x^{5} a+81 a^{2} x^{4}-108 x^{3} a^{3}+81 a^{4} x^{2}-8 a^{3} x^{3}+36 a^{4} x^{2}-54 x^{5}+27 a^{6}`

`=27 x^{6}-54 x^{5} a+117 a^{2} x^{4}-116 a^{3} x^{3}+117 a^{4} x^{2}-54 a^{5} x+27 a^{6}`