Task B-1.2. Write as a power with base 5:

$$
3\left(5^{n}-5\right)\left(5^{n}+5\right)+2\left(25+5^{2 n}\right)+25^{n+1}: 5^{2 n}
$$
## Solution.

$$
\begin{aligned}
& 3\left(5^{n}-5\right)\left(5^{n}+5\right)+2\left(25+5^{2 n}\right)+25^{n+1}: 5^{2 n}= \\
& 3 \cdot\left(5^{2 n}-25\right)+2 \cdot 25+2 \cdot 5^{2 n}+5^{2 n+2}: 5^{2 n}= \\
& 3 \cdot 5^{2 n}-75+50+2 \cdot 5^{2 n}+5^{2}= \\
& 5 \cdot 5^{2 n}=5^{2 n+1}
\end{aligned}
$$