вправа 677 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) a³ + 8 =
= (a + 2)(a² - 2a + 4);
2) c³ - 64 =
= (c - 4)(c² + 4c + 16);
3) 125 - b³ =
= (5 - b)(25 + 5b + b²);
4) 1 + x³ =
= (1 + x)(1 - x + x²);
5) a³ + 1000 =
= (a + 10)(a² - 10a + 100);
6) 27a³ - 1 =
= (3a - 1)(9a² + 3a + 1);
7) 1000c³ - 216 =
= (10c - 6)(100c² + 60c + 36);
8) a³b³ - 1 =
= (ab - 1)(a²b² + ab + 1);
9) m³n³ + 0,001 =
= (mn + 0,1)(m²n² - 0,1mn + 0,01); \begin{equation}10)\frac{64}{343}m^{3}-\frac{125}{216}n^{3}=\end{equation} \begin{equation}=\left ( \frac{4}{7}m-\frac{5}{6}n \right )\end{equation} \begin{equation}\left ( \frac{16}{49}m^{2}+\frac{10}{21}mn+\frac{25}{36}n^{2}; \right )\end{equation} \begin{equation}11)8m^{6}+27n^{9}=\end{equation} \begin{equation}=\left ( 2m^{2}+3n^{3} \right )\end{equation} \begin{equation}\left ( 4m^{4}+6m^{2}n^{3}+9n^{6} \right );\end{equation} \begin{equation}12)m^{6}n^{3}-p^{12}=\end{equation} \begin{equation}=\left ( m^{2}n-p^{4} \right )\end{equation} \begin{equation}\left ( m^{4}n^{2}+m^{2}np^{4}+p^{8} \right );\end{equation} \begin{equation}13)0,027x^{21}+0,125y^{24}=\end{equation} \begin{equation}=\left ( 0,3x^{7}+0,5y^{8} \right )\end{equation} \begin{equation}\left ( 0,09x^{14}-0,15x^{7}y^{8}+0,25y^{16} \right );\end{equation} \begin{equation}14)0,216-8c^{27}=\end{equation} \begin{equation}=\left ( 0,6-2c^{9} \right )\left ( 0,36+1,2c^{9}+4c^{18} \right );\end{equation} \begin{equation}15)1000a^{12}b^{3}+0,001c^{6}d^{15}=\end{equation} \begin{equation}=\left ( 10a^{4}b+0,1c^{2}d^{5} \right )\end{equation} \begin{equation}\left ( 100a^{8}b^{2}-a^{4}bc^{2}d^{5}+0,01c^{4}d^{10} \right ).\end{equation}