展开 ((8x^{10}-1)^8)/(65536x^{48)}

解答

展开

\frac{( 8 x ^{10} - 1 ) ^{8}}{65536 x ^{48}}

256 x^{32} - 256 x^{22} + 112 x^{12} - 28 x^{2} + \frac{35}{8 x ^{8}} - \frac{7}{16 x ^{18}} + \frac{7}{256 x ^{28}} - \frac{1}{1024 x ^{38}} + \frac{1}{65536 x ^{48}}

求解步骤

\frac{( 8 x ^{10} - 1 ) ^{8}}{65536 x ^{48}}

(8 x^{10} - 1)^{8} = 16777216 x^{80} - 16777216 x^{70} + 7340032 x^{60} - 1835008 x^{50} + 286720 x^{40} - 28672 x^{30} + 1792 x^{20} - 64 x^{10} + 1

= \frac{16777216 x ^{80} - 16777216 x ^{70} + 7340032 x ^{60} - 1835008 x ^{50} + 286720 x ^{40} - 28672 x ^{30} + 1792 x ^{20} - 64 x ^{10} + 1}{65536 x ^{48}}

使用分式法则:

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

\frac{16777216 x ^{80} - 16777216 x ^{70} + 7340032 x ^{60} - 1835008 x ^{50} + 286720 x ^{40} - 28672 x ^{30} + 1792 x ^{20} - 64 x ^{10} + 1}{65536 x ^{48}} = \frac{16777216 x ^{80}}{65536 x ^{48}} - \frac{16777216 x ^{70}}{65536 x ^{48}} + \frac{7340032 x ^{60}}{65536 x ^{48}} - \frac{1835008 x ^{50}}{65536 x ^{48}} + \frac{286720 x ^{40}}{65536 x ^{48}} - \frac{28672 x ^{30}}{65536 x ^{48}} + \frac{1792 x ^{20}}{65536 x ^{48}} - \frac{64 x ^{10}}{65536 x ^{48}} + \frac{1}{65536 x ^{48}}

= \frac{16777216 x ^{80}}{65536 x ^{48}} - \frac{16777216 x ^{70}}{65536 x ^{48}} + \frac{7340032 x ^{60}}{65536 x ^{48}} - \frac{1835008 x ^{50}}{65536 x ^{48}} + \frac{286720 x ^{40}}{65536 x ^{48}} - \frac{28672 x ^{30}}{65536 x ^{48}} + \frac{1792 x ^{20}}{65536 x ^{48}} - \frac{64 x ^{10}}{65536 x ^{48}} + \frac{1}{65536 x ^{48}}

\frac{16777216 x ^{80}}{65536 x ^{48}} = 256 x^{32}

\frac{16777216 x ^{70}}{65536 x ^{48}} = 256 x^{22}

\frac{7340032 x ^{60}}{65536 x ^{48}} = 112 x^{12}

\frac{1835008 x ^{50}}{65536 x ^{48}} = 28 x^{2}

\frac{286720 x ^{40}}{65536 x ^{48}} = \frac{35}{8 x ^{8}}

\frac{28672 x ^{30}}{65536 x ^{48}} = \frac{7}{16 x ^{18}}

\frac{1792 x ^{20}}{65536 x ^{48}} = \frac{7}{256 x ^{28}}

\frac{64 x ^{10}}{65536 x ^{48}} = \frac{1}{1024 x ^{38}}

= 256 x^{32} - 256 x^{22} + 112 x^{12} - 28 x^{2} + \frac{35}{8 x ^{8}} - \frac{7}{16 x ^{18}} + \frac{7}{256 x ^{28}} - \frac{1}{1024 x ^{38}} + \frac{1}{65536 x ^{48}}

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