\section*{Exercise 2 - \(341032=340933\)}

Calculate the number

\(123456785 \cdot 123456787 \cdot 123456788 \cdot 123456796 - 123456782 \cdot 123456790 \cdot 123456791 \cdot 123456793\)

without calculating the values of the two products individually!
}

With \(n:=123456789\), the difference

\[
D:=(n-4) \cdot(n-2) \cdot(n-1) \cdot(n+7)-(n-7) \cdot(n+1) \cdot(n+2) \cdot(n+4)
\]

is to be calculated. When expanding the products, the terms with even exponents of \(n\) have the same signs, while those with odd exponents of \(n\) have different signs. Therefore, we get

\[
=2 n^{3} \cdot(-4-2-1+7)+2 n \cdot(-8+56+28+14)=180 n=22.222 .222 .020
\]