展開する ((x^3+2a)^6)/(64x^6)

解

展開する

\frac{( x ^{3} + 2 a ) ^{6}}{64 x ^{6}}

\frac{x ^{12}}{64} + \frac{3 a x ^{9}}{16} + \frac{15 a ^{2} x ^{6}}{16} + \frac{5 a ^{3} x ^{3}}{2} + \frac{15 a ^{4}}{4} + \frac{3 a ^{5}}{x ^{3}} + \frac{a ^{6}}{x ^{6}}

解答ステップ

\frac{( x ^{3} + 2 a ) ^{6}}{64 x ^{6}}

(x^{3} + 2 a)^{6} = x^{18} + 12 a x^{15} + 60 a^{2} x^{12} + 160 a^{3} x^{9} + 240 a^{4} x^{6} + 192 a^{5} x^{3} + 64 a^{6}

= \frac{x ^{18} + 12 a x ^{15} + 60 a ^{2} x ^{12} + 160 a ^{3} x ^{9} + 240 a ^{4} x ^{6} + 192 a ^{5} x ^{3} + 64 a ^{6}}{64 x ^{6}}

分数の規則を適用する:

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

\frac{x ^{18} + 12 a x ^{15} + 60 a ^{2} x ^{12} + 160 a ^{3} x ^{9} + 240 a ^{4} x ^{6} + 192 a ^{5} x ^{3} + 64 a ^{6}}{64 x ^{6}} = \frac{x ^{18}}{64 x ^{6}} + \frac{12 a x ^{15}}{64 x ^{6}} + \frac{60 a ^{2} x ^{12}}{64 x ^{6}} + \frac{160 a ^{3} x ^{9}}{64 x ^{6}} + \frac{240 a ^{4} x ^{6}}{64 x ^{6}} + \frac{192 a ^{5} x ^{3}}{64 x ^{6}} + \frac{64 a ^{6}}{64 x ^{6}}

= \frac{x ^{18}}{64 x ^{6}} + \frac{12 a x ^{15}}{64 x ^{6}} + \frac{60 a ^{2} x ^{12}}{64 x ^{6}} + \frac{160 a ^{3} x ^{9}}{64 x ^{6}} + \frac{240 a ^{4} x ^{6}}{64 x ^{6}} + \frac{192 a ^{5} x ^{3}}{64 x ^{6}} + \frac{64 a ^{6}}{64 x ^{6}}

\frac{x ^{18}}{64 x ^{6}} = \frac{x ^{12}}{64}

\frac{12 a x ^{15}}{64 x ^{6}} = \frac{3 a x ^{9}}{16}

\frac{60 a ^{2} x ^{12}}{64 x ^{6}} = \frac{15 a ^{2} x ^{6}}{16}

\frac{160 a ^{3} x ^{9}}{64 x ^{6}} = \frac{5 a ^{3} x ^{3}}{2}

\frac{240 a ^{4} x ^{6}}{64 x ^{6}} = \frac{15 a ^{4}}{4}

\frac{192 a ^{5} x ^{3}}{64 x ^{6}} = \frac{3 a ^{5}}{x ^{3}}

\frac{64 a ^{6}}{64 x ^{6}} = \frac{a ^{6}}{x ^{6}}

= \frac{x ^{12}}{64} + \frac{3 a x ^{9}}{16} + \frac{15 a ^{2} x ^{6}}{16} + \frac{5 a ^{3} x ^{3}}{2} + \frac{15 a ^{4}}{4} + \frac{3 a ^{5}}{x ^{3}} + \frac{a ^{6}}{x ^{6}}