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

Explanation

Here, given expression is :
\left(55\right)^3-\left(45\right)^3-30\times55\times45
Let’s,
55=a
45=b
Now,
\left(a-b\right)
\rightarrow\left(55-45\right)
\therefore 10
Now, find the value :
\left(55\right)^3-\left(45\right)^3-30\times55\times45
\rightarrow\left(55\right)^3-\left(45\right)^3-3\times10\times55\times45
\rightarrow\left(55\right)^3-\left(45\right)^3-3\times\left(55-45\right)\times55\times45
\rightarrow a^3-b^3-3.\left(a-b\right).a.b
\rightarrow\left(a-b\right)^3
\rightarrow\left(10\right)^3
\therefore 1000
Ans: 1000.