Formula use: \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3

Explanation

Here, given expression is :
3.89\ \times\ 3.89\ \times\ 3.89\ +\ 3\ \times\ 3.89\ \times\ 3.89\ \times\ 1.11\ +\ 3\ \times\ 3.89\ \times\ 1.11\ \times\ 1.11\ +\ 1.11\ \times\ 1.11\ \times\ 1.11
Let,
3.89=a
1.11=b
Now, find the value :
3.89\ \times\ 3.89\ \times\ 3.89\ +\ 3\ \times\ 3.89\ \times\ 3.89\ \times\ 1.11\ +\ 3\ \times\ 3.89\ \times\ 1.11\ \times\ 1.11\ +\ 1.11\ \times\ 1.11\ \times\ 1.11
\rightarrow\left(3.89\right)^3+3\times\left(3.89\right)^2\times\left(1.11\right)+3.89\times\left(1.11\right)^2+\left(1.11\right)^3
\rightarrow a^3+3.a^2.b+3.a.b^2+b^3
\rightarrow\left(a+b\right)^3
Now, putting the a & b value, we get :
\left(3.89+1.11\right)^3
\rightarrow\left(5\right)^3
\therefore 125
Ans: 125.