a) 27n^3

b) 64n^3

c) 125n^3

d) 216n^3

correct answer is: b) 64n^3

Formula use: \left(a-b\right)^3=a^3-b^3-3.a.b.\left(a-b\right)

Explanation

Here, given expression is :
\left(3m+2n\right)^3-\left(3m-2n\right)^3-12(9m^2-4n^2)
\left(3m+2n\right)^3-\left(3m-2n\right)^3-3.4n.(9m^2-4n^2)
Let,
\left(3m+2n\right)=a
\left(3m-2n\right)=b
Now,
\left(a-b\right)
\rightarrow\{\left(3m+2n\right)-\left(3m-2n\right)\}
\rightarrow\left(3m+2n-3m+2n\right)
\therefore 4n
And,
\left(a\times b\right)
\rightarrow\{\left(3m+2n\right)\times\left(3m-2n\right)\}
\rightarrow\{3m\left(3m-2n\right)+2n\left(3m-2n\right)\}
\rightarrow(9m^2-6n+6n-4n^2)
\therefore(9m^2-4n^2)
So,
\left(3m+2n\right)^3-\left(3m-2n\right)^3-3.4n.(9m^2-4n^2)
\rightarrow\left(3m+2n\right)^3-\left(3m-2n\right)^3-3.\{\left(3m+2n\right)-\left(3m-2n\right)\}.\{\left(3m+2n\right)\times\left(3m-2n\right)\}
\rightarrow a^3-b^3-3.\left(a-b\right).a.b
\rightarrow\left(a-b\right)^3
Put the value of \left(a-b\right), we get :
\left(a-b\right)^3
\rightarrow\left(4n\right)^3
\therefore 64n^3
Ans: 64n^3\ .