4) (b2+c2)(b-b2c2+c)-b5(b3+b6).

4) Упростим выражение:

$$\left( b^{\frac{1}{2}} + c^{\frac{1}{2}} \right) \left( b - b^{\frac{1}{2}}c^{\frac{1}{2}} + c \right) - b^{\frac{5}{6}} \left( b^{\frac{2}{3}} + b^{\frac{1}{6}} \right) = $$

$$ = b^{\frac{3}{2}} + c^{\frac{3}{2}} - b^{\frac{5}{6}}b^{\frac{2}{3}} - b^{\frac{5}{6}}b^{\frac{1}{6}} = b^{\frac{3}{2}} + c^{\frac{3}{2}} - b^{\frac{5}{6} + \frac{2}{3}} - b^{\frac{5}{6} + \frac{1}{6}} = b^{\frac{3}{2}} + c^{\frac{3}{2}} - b^{\frac{9}{6}} - b^{\frac{6}{6}} = $$

$$ = b^{\frac{3}{2}} + c^{\frac{3}{2}} - b^{\frac{3}{2}} - b = c^{\frac{3}{2}} - b$$

Ответ: $$c^{\frac{3}{2}} - b$$