Решебник по алгебре 7 класс Мерзляк Задание 677

\[\boxed{\text{677\ (677).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ a³ + 8 =\]

\[= (a + 2)(a^{2} - 2a + 4)\]

\[2)\ c³ - 64 =\]

\[= (c - 4)(c^{2} + 4c + 16)\]

\[3)\ 125 - b^{3} =\]

\[= (5 - b)(25 + 5b + b^{2})\]

\[4)\ 1 + x³ = (1 + x)(1 - x + x^{2})\]

\[5)\ a³ + 1000 =\]

\[= (a + 10)(a^{2} - 10a + 100)\]

\[6)\ 27a³ - 1 =\]

\[= (3a - 1)(9a^{2} + 3a + 1)\]

\[7)\ 1000c³ - 216 =\]

\[= (10c - 6)(100c^{2} + 60c + 36)\]

\[8)\ a³b³ - 1 =\]

\[= (ab - 1)(a^{2}b^{2} + ab + 1)\]

\[9)\ m³n³ + 0,001 =\]

\[= (mn + 0,1)(m^{2}n^{2} - 0,1mn + 0,01)\]

\[10)\frac{64}{343}m³ - \frac{125}{216}n^{3} =\]

\[11)\ 8m^{6} + 27n^{9} =\]

\[= \left( 2m^{2} + 3n^{3} \right)\left( 4m^{4} - 6m^{2}n^{3} + 9n^{6} \right)\]

\[12)\ m^{6}n³ - p^{12} =\]

\[= (m^{2}n - p^{4})(m^{4}n^{2} + m^{2}np^{4} + p^{8})\]

\[13)\ 0,027x^{21} + 0,125y^{24} =\]

\[14)\ 0,216 - 8c^{27} =\]

\[= (0,6 - 2c^{9})(0,36 + 1,2c^{9} + 4c^{18})\]

\[15)\ 1000a^{12}b³ + 0,001c^{6}d^{15} =\]