espandere ((8x^{10}-1)^8)/(65536x^{48)}

Soluzione

espandere

\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}}

Fasi della soluzione

\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}}

Applica la regola delle frazioni:

\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}}

e x p an d e^{- 4 t - 8} h (t - 2)

e x p an d sin (3 (180 - θ))

e x p an d lo g_{7} (5 x)

\frac{\partial}{\partial y} ((z) (x^{2} - 3 x y + y^{2}))

e x p an d \frac{d}{d x} ((8 x + 3) (x^{2} - 1)) + \frac{x + 4}{5}