ГДЗ по алгебре 7 класс Абылкасымова параграф 31 - 31.5

1) $13^2 - 9^2 = (13 - 9)(13 + 9) = 4 \cdot 22 = 88$ 2) $20^2 - 19^2 = (20 - 19)(20 + 19) = 1 \cdot 39 = 39$ 3) $2,2^2 - 2,8^2 = (2,2 - 2,8)(2,2 + 2,8) = -0,6 \cdot 5 = -3$ 4) $3,5^2 - 3,7^2 = (3,5 - 3,7)(3,5 + 3,7) = -0,2 \cdot 7,2 = -1,44$ 5) $\left(\frac{5}{6}\right)^2 - \left(\frac{2}{3}\right)^2 = \left(\frac{5}{6} - \frac{2}{3}\right)\left(\frac{5}{6} + \frac{2}{3}\right) = \left(\frac{5}{6} - \frac{4}{6}\right)\left(\frac{5}{6} + \frac{4}{6}\right) = \frac{1}{6} \cdot \frac{9}{6} = \frac{1}{6} \cdot \frac{3}{2} = \frac{1}{4}$ 6) $\left(\frac{7}{9}\right)^2 - \left(\frac{1}{6}\right)^2 = \left(\frac{7}{9} - \frac{1}{6}\right)\left(\frac{7}{9} + \frac{1}{6}\right) = \left(\frac{14}{18} - \frac{3}{18}\right)\left(\frac{14}{18} + \frac{3}{18}\right) = \frac{11}{18} \cdot \frac{17}{18} = \frac{187}{324}$ 7) $\left(\frac{5}{12}\right)^2 - \left(\frac{3}{4}\right)^2 = \left(\frac{5}{12} - \frac{3}{4}\right)\left(\frac{5}{12} + \frac{3}{4}\right) = \left(\frac{5}{12} - \frac{9}{12}\right)\left(\frac{5}{12} + \frac{9}{12}\right) = -\frac{4}{12} \cdot \frac{14}{12} = -\frac{1}{3} \cdot \frac{7}{6} = -\frac{7}{18}$ 8) $\left(\frac{3}{10}\right)^2 - \left(\frac{4}{5}\right)^2 = \left(\frac{3}{10} - \frac{4}{5}\right)\left(\frac{3}{10} + \frac{4}{5}\right) = \left(\frac{3}{10} - \frac{8}{10}\right)\left(\frac{3}{10} + \frac{8}{10}\right) = -\frac{5}{10} \cdot \frac{11}{10} = -\frac{1}{2} \cdot \frac{11}{10} = -\frac{11}{20} = -0,55$ 9) $\left(\frac{8}{15}\right)^2 - \left(\frac{4}{5}\right)^2 = \left(\frac{8}{15} - \frac{4}{5}\right)\left(\frac{8}{15} + \frac{4}{5}\right) = \left(\frac{8}{15} - \frac{12}{15}\right)\left(\frac{8}{15} + \frac{12}{15}\right) = -\frac{4}{15} \cdot \frac{20}{15} = -\frac{4}{15} \cdot \frac{4}{3} = -\frac{16}{45}$ 10) $\left(2\frac{1}{7}\right)^2 - \left(2\frac{1}{7}\right)^2 = \left(2\frac{1}{7} - 2\frac{1}{7}\right)\left(2\frac{1}{7} + 2\frac{1}{7}\right) = 0 \cdot 4\frac{2}{7} = 0$ 11) $\left(3\frac{1}{3}\right)^2 - \left(4\frac{1}{2}\right)^2 = \left(\frac{10}{3}\right)^2 - \left(\frac{9}{2}\right)^2 = \left(\frac{10}{3} - \frac{9}{2}\right)\left(\frac{10}{3} + \frac{9}{2}\right) = \left(\frac{20}{6} - \frac{27}{6}\right)\left(\frac{20}{6} + \frac{27}{6}\right) = -\frac{7}{6} \cdot \frac{47}{6} = -\frac{329}{36} = -9\frac{5}{36}$ 12) $\left(5\frac{1}{6}\right)^2 - \left(7\frac{1}{3}\right)^2 = \left(\frac{31}{6}\right)^2 - \left(\frac{22}{3}\right)^2 = \left(\frac{31}{6} - \frac{22}{3}\right)\left(\frac{31}{6} + \frac{22}{3}\right) = \left(\frac{31}{6} - \frac{44}{6}\right)\left(\frac{31}{6} + \frac{44}{6}\right) = -\frac{13}{6} \cdot \frac{75}{6} = -\frac{13}{2} \cdot \frac{25}{6} = -\frac{325}{12} = -27\frac{1}{12}$ 13) $51^2 - 41^2 = (51 - 41)(51 + 41) = 10 \cdot 92 = 920$ 14) $54^2 - 46^2 = (54 - 46)(54 + 46) = 8 \cdot 100 = 800$ 15) $76^2 - 24^2 = (76 - 24)(76 + 24) = 52 \cdot 100 = 5200$ 16) $328^2 - 172^2 = (328 - 172)(328 + 172) = 156 \cdot 500 = 78000$ 17) $\left(3\frac{2}{3}\right)^2 - \left(2\frac{1}{3}\right)^2 = \left(3\frac{2}{3} - 2\frac{1}{3}\right)\left(3\frac{2}{3} + 2\frac{1}{3}\right) = 1\frac{1}{3} \cdot 6 = \frac{4}{3} \cdot 6 = 8$ 18) $\left(7\frac{5}{9}\right)^2 - \left(4\frac{4}{9}\right)^2 = \left(7\frac{5}{9} - 4\frac{4}{9}\right)\left(7\frac{5}{9} + 4\frac{4}{9}\right) = 3\frac{1}{9} \cdot 12 = \frac{28}{9} \cdot 12 = \frac{28 \cdot 4}{3} = \frac{112}{3} = 37\frac{1}{3}$