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

Explanation

Here, given equation is :
\left(5x-2\right)^3+\left(3-4x\right)^3+3.\left(x+1\right).\left(5x-2\right).\left(3-4x\right)
Let,
\left(5x-2\right)=a
\left(3-4x\right)=b

If we add a and b then we get :
\{\left(5x-2\right)+\left(3-4x\right)\}=\left(5x-2+3-4x\right)=\left(x+1\right) _—-(1)
Now, Simplify the equation :
\left(5x-2\right)^3+\left(3-4x\right)^3+3.\left(x+1\right).\left(5x-2\right).\left(3-4x\right)
Or, \left(5x-2\right)^3+\left(3-4x\right)^3+3.\left(5x-2\right).\left(3-4x\right)\{\left(5x-2\right)+\left(3-4x\right)\} _{[from (1)]}
Now, putting the a & b value, we get :
a^3+b^3+3.a.b\left(a+b\right)
\rightarrow\left(a+b\right)^3
\therefore Putting the value :
\{\left(5x-2\right)+\left(3-4x\right)\}^3
\rightarrow\left(5x-2+3-4x\right)^3
\rightarrow\left(x+1\right)^3
\rightarrow\left(x\right)^3+3.x^2.1+3.x.\left(1\right)^2+\left(1\right)^3
\rightarrow x^3+3x^2+3x+1
Ans: x^3+3x^2+3x+1\ .