Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 17

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\[1)\ \left( 8x - y^{2} \right)\left( 3x + y^{2} \right) = 24x^{2} -\]

\[- 3xy^{2} + 8xy^{2} - y^{4} = 24x^{2} +\]

\[+ 5xy^{2} - y^{4}\]

\[2)\ \left( 2m^{2}n - 5mn^{2} \right) \cdot\]

\[\cdot \left( 3mn^{2} - 4m^{2}n \right) =\]

\[= 6m^{3}n^{3} - 15m^{2}n^{4} - 8m^{4}n^{2} +\]

\[+ 20m^{3}n^{3} = - 8m^{4}n^{2} -\]

\[- 15m^{2}n^{4} + 26m^{3}n^{3}\]

\[3)\ \left( 5xy^{2} - 2x^{2}y \right)\left( 2x^{2}y + 5xy^{2} \right) =\]

\[= 25x^{2}y^{4} - 4x^{4}y^{2}\]

\[4)\ \left( \frac{1}{2}a^{3} + b^{2} \right)\left( b^{2} - \frac{1}{2}a^{3} \right) =\]

\[= b^{4} - \frac{1}{4}a^{6}\]

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

\[= a^{9} + b^{9}\]

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

\[= 27m^{6} - n^{6}\]