展開する ((x^7+4)^7)/(128x^{14)}

解

展開する

\frac{( x ^{7} + 4 ) ^{7}}{128 x ^{14}}

\frac{x ^{35}}{128} + \frac{7 x ^{28}}{32} + \frac{21 x ^{21}}{8} + \frac{35 x ^{14}}{2} + 70 x^{7} + 168 + \frac{224}{x ^{7}} + \frac{128}{x ^{14}}

解答ステップ

\frac{( x ^{7} + 4 ) ^{7}}{128 x ^{14}}

(x^{7} + 4)^{7} = x^{49} + 28 x^{42} + 336 x^{35} + 2240 x^{28} + 8960 x^{21} + 21504 x^{14} + 28672 x^{7} + 16384

= \frac{x ^{49} + 28 x ^{42} + 336 x ^{35} + 2240 x ^{28} + 8960 x ^{21} + 21504 x ^{14} + 28672 x ^{7} + 16384}{128 x ^{14}}

分数の規則を適用する:

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

\frac{x ^{49} + 28 x ^{42} + 336 x ^{35} + 2240 x ^{28} + 8960 x ^{21} + 21504 x ^{14} + 28672 x ^{7} + 16384}{128 x ^{14}} = \frac{x ^{49}}{128 x ^{14}} + \frac{28 x ^{42}}{128 x ^{14}} + \frac{336 x ^{35}}{128 x ^{14}} + \frac{2240 x ^{28}}{128 x ^{14}} + \frac{8960 x ^{21}}{128 x ^{14}} + \frac{21504 x ^{14}}{128 x ^{14}} + \frac{28672 x ^{7}}{128 x ^{14}} + \frac{16384}{128 x ^{14}}

= \frac{x ^{49}}{128 x ^{14}} + \frac{28 x ^{42}}{128 x ^{14}} + \frac{336 x ^{35}}{128 x ^{14}} + \frac{2240 x ^{28}}{128 x ^{14}} + \frac{8960 x ^{21}}{128 x ^{14}} + \frac{21504 x ^{14}}{128 x ^{14}} + \frac{28672 x ^{7}}{128 x ^{14}} + \frac{16384}{128 x ^{14}}

\frac{x ^{49}}{128 x ^{14}} = \frac{x ^{35}}{128}

\frac{28 x ^{42}}{128 x ^{14}} = \frac{7 x ^{28}}{32}

\frac{336 x ^{35}}{128 x ^{14}} = \frac{21 x ^{21}}{8}

\frac{2240 x ^{28}}{128 x ^{14}} = \frac{35 x ^{14}}{2}

\frac{8960 x ^{21}}{128 x ^{14}} = 70 x^{7}

\frac{21504 x ^{14}}{128 x ^{14}} = 168

\frac{28672 x ^{7}}{128 x ^{14}} = \frac{224}{x ^{7}}

\frac{16384}{128 x ^{14}} = \frac{128}{x ^{14}}

= \frac{x ^{35}}{128} + \frac{7 x ^{28}}{32} + \frac{21 x ^{21}}{8} + \frac{35 x ^{14}}{2} + 70 x^{7} + 168 + \frac{224}{x ^{7}} + \frac{128}{x ^{14}}