\[*\ - \frac{1}{3}bc + \frac{1}{9}c^{2} =\]
\[= \frac{1}{4}b^{2} - \frac{1}{3}bc + \frac{1}{9}c^{2} =\]
\[= \left( \frac{1}{2}b - \frac{1}{3}c \right)^{2}\]