Приведем подобные члены многочлена: $$\frac{1}{5} a^2b^2 + \frac{2}{5} a^2b + \frac{3}{5} ab^2 + \frac{4}{5} a^2b^2 = (\frac{1}{5} + \frac{4}{5})a^2b^2 + \frac{2}{5}a^2b + \frac{3}{5}ab^2 = \frac{5}{5}a^2b^2 + \frac{2}{5}a^2b + \frac{3}{5}ab^2 = a^2b^2 + \frac{2}{5}a^2b + \frac{3}{5}ab^2$$.
Ответ: $$a^2b^2 + \frac{2}{5}a^2b + \frac{3}{5}ab^2$$