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

Explanation

Here, given expression is :
\left(55\right)^3+3\times\left(55\right)^2\times45+3\times55\times\left(45\right)^2+\left(45\right)^3
Let,
55=a
45=b
Now, find the value :
\left(55\right)^3+3\times\left(55\right)^2\times45+3\times55\times\left(45\right)^2+\left(45\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(55+45\right)^3
\rightarrow\left(100\right)^3
\therefore 1000000
Ans: 1000000.