展開する ((2x^3-3)^6)/(36x^2)

解

展開する

\frac{( 2 x ^{3} - 3 ) ^{6}}{36 x ^{2}}

\frac{16 x ^{16}}{9} - 16 x^{13} + 60 x^{10} - 120 x^{7} + 135 x^{4} - 81 x + \frac{81}{4 x ^{2}}

解答ステップ

\frac{( 2 x ^{3} - 3 ) ^{6}}{36 x ^{2}}

(2 x^{3} - 3)^{6} = 64 x^{18} - 576 x^{15} + 2160 x^{12} - 4320 x^{9} + 4860 x^{6} - 2916 x^{3} + 729

= \frac{64 x ^{18} - 576 x ^{15} + 2160 x ^{12} - 4320 x ^{9} + 4860 x ^{6} - 2916 x ^{3} + 729}{36 x ^{2}}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{64 x ^{18} - 576 x ^{15} + 2160 x ^{12} - 4320 x ^{9} + 4860 x ^{6} - 2916 x ^{3} + 729}{36 x ^{2}} = \frac{64 x ^{18}}{36 x ^{2}} - \frac{576 x ^{15}}{36 x ^{2}} + \frac{2160 x ^{12}}{36 x ^{2}} - \frac{4320 x ^{9}}{36 x ^{2}} + \frac{4860 x ^{6}}{36 x ^{2}} - \frac{2916 x ^{3}}{36 x ^{2}} + \frac{729}{36 x ^{2}}

= \frac{64 x ^{18}}{36 x ^{2}} - \frac{576 x ^{15}}{36 x ^{2}} + \frac{2160 x ^{12}}{36 x ^{2}} - \frac{4320 x ^{9}}{36 x ^{2}} + \frac{4860 x ^{6}}{36 x ^{2}} - \frac{2916 x ^{3}}{36 x ^{2}} + \frac{729}{36 x ^{2}}

\frac{64 x ^{18}}{36 x ^{2}} = \frac{16 x ^{16}}{9}

\frac{576 x ^{15}}{36 x ^{2}} = 16 x^{13}

\frac{2160 x ^{12}}{36 x ^{2}} = 60 x^{10}

\frac{4320 x ^{9}}{36 x ^{2}} = 120 x^{7}

\frac{4860 x ^{6}}{36 x ^{2}} = 135 x^{4}

\frac{2916 x ^{3}}{36 x ^{2}} = 81 x

\frac{729}{36 x ^{2}} = \frac{81}{4 x ^{2}}

= \frac{16 x ^{16}}{9} - 16 x^{13} + 60 x^{10} - 120 x^{7} + 135 x^{4} - 81 x + \frac{81}{4 x ^{2}}