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

Explanation

Here, given equation is :
\left(3p-7q\right)^3+\left(7q+p\right)^3+12p\left(3p-7q\right)\left(7q+p\right)
Let,
a=\left(3p-7q\right)
b=\left(7q+p\right)
If we add a and b then we get :
\left(a+b\right)
\rightarrow\{\left(3p-7q\right)+\left(7q+p\right)\}
\rightarrow\left(3p-7q+7q+p\right)
\therefore\left(4p\right)
\therefore We know, \left(a+b\right)=4p _——(1)
Now, Simplify the equation :
\left(3p-7q\right)^3+\left(7q+p\right)^3+12p\left(3p-7q\right)\left(7q+p\right)
Or, \left(3p-7q\right)^3+\left(7q+p\right)^3+3.4p.\left(3p-7q\right)\left(7q+p\right)
Or, \left(3p-7q\right)^3+\left(7q+p\right)^3+3.\{\left(3p-7q\right)+\left(7q+p\right)\}.\left(3p-7q\right)\left(7q+p\right) _[(a+b)=4p]
Now, putting the a & b value, we get :
a^3+b^3+3.ab.\left(a+b\right)
\therefore\left(a+b\right)^3

So that, Putting the value :
\left(4p\right)^3 _{[from 1, (a+b)=4p]}
\therefore 64p^3
Ans: 64p^3.