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25n^{2}+5n\left(-\frac{1}{5}\right)-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)
Apply the distributive property by multiplying each term of 5n-\frac{4}{5} by each term of 5n-\frac{1}{5}.
25n^{2}-n-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)
Cancel out 5 and 5.
25n^{2}-n-4n-\frac{4}{5}\left(-\frac{1}{5}\right)
Cancel out 5 and 5.
25n^{2}-5n-\frac{4}{5}\left(-\frac{1}{5}\right)
Combine -n and -4n to get -5n.
25n^{2}-5n+\frac{-4\left(-1\right)}{5\times 5}
Multiply -\frac{4}{5} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.
25n^{2}-5n+\frac{4}{25}
Do the multiplications in the fraction \frac{-4\left(-1\right)}{5\times 5}.
25n^{2}+5n\left(-\frac{1}{5}\right)-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)
Apply the distributive property by multiplying each term of 5n-\frac{4}{5} by each term of 5n-\frac{1}{5}.
25n^{2}-n-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)
Cancel out 5 and 5.
25n^{2}-n-4n-\frac{4}{5}\left(-\frac{1}{5}\right)
Cancel out 5 and 5.
25n^{2}-5n-\frac{4}{5}\left(-\frac{1}{5}\right)
Combine -n and -4n to get -5n.
25n^{2}-5n+\frac{-4\left(-1\right)}{5\times 5}
Multiply -\frac{4}{5} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.
25n^{2}-5n+\frac{4}{25}
Do the multiplications in the fraction \frac{-4\left(-1\right)}{5\times 5}.