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

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

#### Explanation

*Here,* given equation is :

\left(3-7m\right)^3+\left(8m-1\right)^3+3\left(m+2\right)\left(3-7m\right)\left(8m-1\right) *Let,*

\left(3-7m\right)=a

\left(8m-1\right)=b

If we add a and b then we get :

\left(a+b\right)

\rightarrow\{\left(3-7m\right)+\left(8m-1\right)\}

\rightarrow\left(3-7m+8m-1\right)

\therefore\left(m+2\right) _{——(1)}*Now,* Simplify the equation :

\left(3-7m\right)^3+\left(8m-1\right)^3+3\left(m+2\right)\left(3-7m\right)\left(8m-1\right)

\rightarrow\left(3-7m\right)^3+\left(8m-1\right)^3+3.\{\left(3-7m\right)+\left(8m-1\right)\}.\left(3-7m\right)\left(8m-1\right) _{[(a+b)=(m+2)]}*Now,* putting the a & b value, we get :

a^3+b^3+3.\left(a+b\right).ab

\therefore\left(a+b\right)^3 *So that,* Putting the value :

\left(m+2\right)^3 _{[from 1, (a+b)=(m+2)]}*Or,* m^3+\left(2\right)^3+3.m.2.\left(m+2\right) *Or,* m^3+8+6m.\left(m+2\right)

\therefore m^3+8+6m^2+12m **Ans:** m^3+6m^2+12m+8\ .