To solve the expression \( 357 \times 25 + 357 \times 74 + 357 \), we can factor out the common term \( 357 \):

\[
357 \times 25 + 357 \times 74 + 357 = 357 \times (25 + 74 + 1)
\]

First, we add the numbers inside the parentheses:

\[
25 + 74 + 1 = 100
\]

Now, we multiply \( 357 \) by \( 100 \):

\[
357 \times 100 = 35700
\]

So, the value of the expression is:

\[
357 \times 25 + 357 \times 74 + 357 = 35700
\]