Решебник по алгебре 7 класс Мерзляк Задание 503

\[\boxed{\text{503\ (503).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \left( x^{3} + 4 \right)\left( x^{3} - 4 \right) =\]

\[= \left( x^{3} \right)^{2} - 4^{2} = x^{6} - 16\]

\[2)\ (ab - c)(ab + c) =\]

\[= \left( \text{ab} \right)^{2} - c^{2} = a^{2}b^{2} - c^{2}\]

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

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

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

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

\[5)\ \left( 6a^{3} - 8b \right)\left( 6a^{3} + 8b \right) =\]

\[= \left( 6a^{3} \right)^{2} - (8b)^{2} =\]

\[= 36a^{6} - 64b^{2}\]

\[6)\ \left( 5n^{4} - m^{4} \right)\left( 5n^{4} + m^{4} \right) =\]

\[= \left( 5n^{4} \right)^{2} - \left( m^{4} \right)^{2} = 25n^{8} - m^{8}\]

\[= \left( 0,2m^{8} \right)^{2} - \left( 0,8n^{6} \right)^{2} =\]

\[= 0,04m^{16} - 0,64n^{12}\]

\[= \left( \frac{4}{11}k^{9} \right)^{2} - \left( \frac{2}{7}p^{7} \right)^{2} =\]

\[= \frac{16}{121}k^{18} - \frac{4}{49}p^{14}\]