Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 330

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\[1)\ \left( 243x^{5} - 32 \right)\ :(3x - 2) =\]

\[= 243 \cdot \left( x^{5} - \frac{32}{243} \right)\ :(3x - 2) =\]

\[= 243 \cdot \left( x^{5} - \left( \frac{2}{3} \right)^{5} \right)\ :\]

\[:3 \cdot \left( x - \frac{2}{3} \right) =\]

\[= \frac{243}{3} \cdot \left( x^{4} + \frac{2}{3}x^{3} + \frac{4}{9}x^{2} + \frac{8}{24}x + \frac{16}{81} \right) =\]

\[= 81x^{4} + 54x^{3} + 36x^{2} +\]

\[+ 24x + 16.\]

\[2)\ \left( a^{4}x^{4} - b^{4} \right)\ :(ax - b) =\]

\[= a^{4}\left( x^{4} - \left( \frac{b}{a} \right)^{4} \right)\ :a\left( x - \frac{b}{a} \right) =\]

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

\[= a^{3}x^{3} - a^{2}bx + ab^{2}x - b^{3}.\]

\[3)\ \left( x^{30} + 1 \right)\ :\left( x^{5} + 1 \right) =\]

\[= x^{25} - x^{20} + x^{15} -\]

\[- x^{10} + x^{5} - 1.\]

\[4)\ \left( 3\frac{3}{8}a^{6} + 8b^{12} \right)\ :\]

\[:\left( 1,5a^{2} + 2b^{4} \right) =\]

\[= \left( \frac{27}{8}a^{6} + 8b^{12} \right)\ :\]

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

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

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

\[= \left( \frac{3}{2}a^{2} + 2b^{4} \right)\left( \frac{9}{4}a^{4} - 3a^{2}b^{4} + 4b^{8} \right)\ :\]

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

\[= \frac{9}{4}a^{4} - 3a^{2}b^{4} + 4b^{8}.\]