desarrollar ((2x^8+3)^8)/(128)

Solución

desarrollar

\frac{( 2 x ^{8} + 3 ) ^{8}}{128}

2 x^{64} + 24 x^{56} + 126 x^{48} + 378 x^{40} + \frac{2835 x ^{32}}{4} + \frac{1701 x ^{24}}{2} + \frac{5103 x ^{16}}{8} + \frac{2187 x ^{8}}{8} + \frac{6561}{128}

Pasos de solución

\frac{( 2 x ^{8} + 3 ) ^{8}}{128}

(2 x^{8} + 3)^{8} = 256 x^{64} + 3072 x^{56} + 16128 x^{48} + 48384 x^{40} + 90720 x^{32} + 108864 x^{24} + 81648 x^{16} + 34992 x^{8} + 6561

= \frac{256 x ^{64} + 3072 x ^{56} + 16128 x ^{48} + 48384 x ^{40} + 90720 x ^{32} + 108864 x ^{24} + 81648 x ^{16} + 34992 x ^{8} + 6561}{128}

Aplicar las propiedades de las fracciones:

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

\frac{256 x ^{64} + 3072 x ^{56} + 16128 x ^{48} + 48384 x ^{40} + 90720 x ^{32} + 108864 x ^{24} + 81648 x ^{16} + 34992 x ^{8} + 6561}{128} = \frac{256 x ^{64}}{128} + \frac{3072 x ^{56}}{128} + \frac{16128 x ^{48}}{128} + \frac{48384 x ^{40}}{128} + \frac{90720 x ^{32}}{128} + \frac{108864 x ^{24}}{128} + \frac{81648 x ^{16}}{128} + \frac{34992 x ^{8}}{128} + \frac{6561}{128}

= \frac{256 x ^{64}}{128} + \frac{3072 x ^{56}}{128} + \frac{16128 x ^{48}}{128} + \frac{48384 x ^{40}}{128} + \frac{90720 x ^{32}}{128} + \frac{108864 x ^{24}}{128} + \frac{81648 x ^{16}}{128} + \frac{34992 x ^{8}}{128} + \frac{6561}{128}

\frac{256 x ^{64}}{128} = 2 x^{64}

\frac{3072 x ^{56}}{128} = 24 x^{56}

\frac{16128 x ^{48}}{128} = 126 x^{48}

\frac{48384 x ^{40}}{128} = 378 x^{40}

\frac{90720 x ^{32}}{128} = \frac{2835 x ^{32}}{4}

\frac{108864 x ^{24}}{128} = \frac{1701 x ^{24}}{2}

\frac{81648 x ^{16}}{128} = \frac{5103 x ^{16}}{8}

\frac{34992 x ^{8}}{128} = \frac{2187 x ^{8}}{8}

= 2 x^{64} + 24 x^{56} + 126 x^{48} + 378 x^{40} + \frac{2835 x ^{32}}{4} + \frac{1701 x ^{24}}{2} + \frac{5103 x ^{16}}{8} + \frac{2187 x ^{8}}{8} + \frac{6561}{128}

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