展开 ((4-m^3)^7)/(128m^7)

解答

展开

\frac{( 4 - m ^{3} ) ^{7}}{128 m ^{7}}

\frac{128}{m ^{7}} - \frac{224}{m ^{4}} + \frac{168}{m} - 70 m^{2} + \frac{35 m ^{5}}{2} - \frac{21 m ^{8}}{8} + \frac{7 m ^{11}}{32} - \frac{m ^{14}}{128}

求解步骤

\frac{( 4 - m ^{3} ) ^{7}}{128 m ^{7}}

(4 - m^{3})^{7} = 16384 - 28672 m^{3} + 21504 m^{6} - 8960 m^{9} + 2240 m^{12} - 336 m^{15} + 28 m^{18} - m^{21}

= \frac{16384 - 28672 m ^{3} + 21504 m ^{6} - 8960 m ^{9} + 2240 m ^{12} - 336 m ^{15} + 28 m ^{18} - m ^{21}}{128 m ^{7}}

使用分式法则:

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

\frac{16384 - 28672 m ^{3} + 21504 m ^{6} - 8960 m ^{9} + 2240 m ^{12} - 336 m ^{15} + 28 m ^{18} - m ^{21}}{128 m ^{7}} = \frac{16384}{128 m ^{7}} - \frac{28672 m ^{3}}{128 m ^{7}} + \frac{21504 m ^{6}}{128 m ^{7}} - \frac{8960 m ^{9}}{128 m ^{7}} + \frac{2240 m ^{12}}{128 m ^{7}} - \frac{336 m ^{15}}{128 m ^{7}} + \frac{28 m ^{18}}{128 m ^{7}} - \frac{m ^{21}}{128 m ^{7}}

= \frac{16384}{128 m ^{7}} - \frac{28672 m ^{3}}{128 m ^{7}} + \frac{21504 m ^{6}}{128 m ^{7}} - \frac{8960 m ^{9}}{128 m ^{7}} + \frac{2240 m ^{12}}{128 m ^{7}} - \frac{336 m ^{15}}{128 m ^{7}} + \frac{28 m ^{18}}{128 m ^{7}} - \frac{m ^{21}}{128 m ^{7}}

\frac{16384}{128 m ^{7}} = \frac{128}{m ^{7}}

\frac{28672 m ^{3}}{128 m ^{7}} = \frac{224}{m ^{4}}

\frac{21504 m ^{6}}{128 m ^{7}} = \frac{168}{m}

\frac{8960 m ^{9}}{128 m ^{7}} = 70 m^{2}

\frac{2240 m ^{12}}{128 m ^{7}} = \frac{35 m ^{5}}{2}

\frac{336 m ^{15}}{128 m ^{7}} = \frac{21 m ^{8}}{8}

\frac{28 m ^{18}}{128 m ^{7}} = \frac{7 m ^{11}}{32}

\frac{m ^{21}}{128 m ^{7}} = \frac{m ^{14}}{128}

= \frac{128}{m ^{7}} - \frac{224}{m ^{4}} + \frac{168}{m} - 70 m^{2} + \frac{35 m ^{5}}{2} - \frac{21 m ^{8}}{8} + \frac{7 m ^{11}}{32} - \frac{m ^{14}}{128}

e x p an d \frac{e ^{- 2 s} ( s + 11 )}{( s + 5 ) ( s + 4 )}

e x p an d \frac{( 3 x ^{2} - 2 ) d y}{d x} + 6 x y

e x p an d ((y + 2 x) d y + d x) e^{2 y}

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{3} - 3 y^{2}))

e x p an d (x - 4) (x - 2 + 7)