32.6.1) \(\frac{4}{9} + \frac{4}{3}a + a^{2};\) 3) \(\frac{16}{49} + \frac{8}{7}c + c^{2};\) 5) \(m^{2} - \frac{22}{13}mn + \frac{121}{169}n^{2};\) 32.7. 1) \(\frac{25}{4} + 5x + x^{2};\) 3) \(\frac{49}{36} - \frac{7}{3}z + z^{2};\) 5) \(m^{2} + \frac{11}{6}m + \frac{121}{144};\)

32.6.

1. $$\frac{4}{9} + \frac{4}{3}a + a^{2} = (\frac{2}{3})^{2} + 2 \cdot \frac{2}{3} \cdot a + a^{2} = (\frac{2}{3} + a)^{2}$$ Ответ: $$(\frac{2}{3} + a)^{2}$$
2. $$\frac{16}{49} + \frac{8}{7}c + c^{2} = (\frac{4}{7})^{2} + 2 \cdot \frac{4}{7} \cdot c + c^{2} = (\frac{4}{7} + c)^{2}$$ Ответ: $$(\frac{4}{7} + c)^{2}$$
3. $$m^{2} - \frac{22}{13}mn + \frac{121}{169}n^{2} = m^{2} - 2 \cdot m \cdot \frac{11}{13}n + (\frac{11}{13}n)^{2} = (m - \frac{11}{13}n)^{2}$$ Ответ: $$(m - \frac{11}{13}n)^{2}$$

32.7.

1. $$\frac{25}{4} + 5x + x^{2} = (\frac{5}{2})^{2} + 2 \cdot \frac{5}{2} \cdot x + x^{2} = (\frac{5}{2} + x)^{2}$$ Ответ: $$(\frac{5}{2} + x)^{2}$$
2. $$\frac{49}{36} - \frac{7}{3}z + z^{2} = (\frac{7}{6})^{2} - 2 \cdot \frac{7}{6} \cdot z + z^{2} = (\frac{7}{6} - z)^{2}$$ Ответ: $$(\frac{7}{6} - z)^{2}$$
3. $$m^{2} + \frac{11}{6}m + \frac{121}{144} = m^{2} + 2 \cdot m \cdot \frac{11}{12} + (\frac{11}{12})^{2} = (m + \frac{11}{12})^{2}$$ Ответ: $$(m + \frac{11}{12})^{2}$$