Решебник по алгебре 7 класс Мерзляк ФГОС Задание 697

 

\[\boxed{\text{697\ (697).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x^{6} + 3x^{2}y^{2} + y^{6} =\]

\[= \left( x^{6} + y^{6} \right) + 3x^{2}y^{2} =\]

\[= x^{4} - x^{2}y^{2} + y^{4} + 3x^{2}y^{2} =\]

\[= x^{4} + 2x^{2}y^{2} + y^{4} =\]

\[= \left( x^{2} + y^{2} \right)^{2} = 1^{2} = 1\]

\[Ответ:1.\]

\[\boxed{\text{697.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (2m + 1)^{2} = 4m^{2} + 4m + 1\]

\[2)\ (4x - 3)^{2} = 16x^{2} - 24x + 9\]

\[3)\ (10c + 9d)^{2} =\]

\[= 100c^{2} + 180cd + 81d^{2}\]

\[4)\ \left( 4x - \frac{1}{8}y \right)^{2} =\]

\[= 16x^{2} - xy + \frac{1}{64}y^{2}\]

\[5)\ (0,3a + 0,9b)^{2} =\]

\[= 0,09a^{2} + 0,54ab + 0,81b^{2}\]

\[6)\ \left( c^{2} - 6 \right)^{2} = c^{4} - 12c^{2} + 36\]

\[7)\ \left( m^{2} - 3n \right)^{2} = m^{4} - 6m^{2}n + 9n^{2}\]

\[8)\ \left( m^{4} - n^{3} \right)^{2} = m^{8} - 2m^{4}n^{3} + n^{6}\]

\[9)\ \left( 5a^{4} - 2a^{7} \right)^{2} =\]

\[= 25a^{8} - 20a^{11} + 4a^{14}\]