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Popular Álgebra >

desarrollar (6-\sqrt[4]{x/(362797056)})^{17}

Solución

desarrollar

(6 - 4 \frac{x}{362797056})^{17}

Solución

6^{17} - 6^{13} \cdot 1746 4 x + 6^{15} \cdot 136 (4 \frac{x}{362797056})^{2} - 6^{14} \cdot 680 (4 \frac{x}{362797056})^{3} + 85680 x - 37128 x 4 \frac{x}{362797056} + \frac{1547 x x}{972 6} - \frac{9724 x 4 x ^{3}}{3 4 36279705 6 ^{3}} + \frac{12155 x ^{2}}{6530347008} - \frac{12155 x ^{2} 4 \frac{x}{362797056}}{39182082048} + \frac{2431 x ^{2} x}{58773123072 362797056} - \frac{1547 x ^{2} 4 x ^{3}}{373248 \cdot 97 2 ^{2} 4 36279705 6 ^{3}} + \frac{1547 x ^{3}}{3 ^{28} \cdot 67108864} - \frac{595 x ^{3} 4 \frac{x}{362797056}}{518 4 ^{2} \cdot 6998 4 ^{3}} + \frac{85 x ^{3} x}{172 8 ^{2} \cdot 20995 2 ^{3} 362797056} - \frac{17 x ^{3} 4 x ^{3}}{28 8 ^{5} \cdot 437 4 ^{3} 4 36279705 6 ^{3}} + \frac{17 x ^{4}}{6 ^{43}} - \frac{x ^{4} 4 \frac{x}{362797056}}{36279705 6 ^{4}}

Pasos de solución

(6 - 4 \frac{x}{362797056})^{17}

Aplicar el teorema del binomio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 6, b = - 4 \frac{x}{362797056}

= i = 0 \sum 17 (i 17) \cdot 6^{(17 - i)} (- 4 \frac{x}{362797056})^{i}

Expandir sumatorio

= \frac{17 !}{0 ! ( 17 - 0 ) !} \cdot 6^{17} (- 4 \frac{x}{362797056})^{0} + \frac{17 !}{1 ! ( 17 - 1 ) !} \cdot 6^{16} (- 4 \frac{x}{362797056})^{1} + \frac{17 !}{2 ! ( 17 - 2 ) !} \cdot 6^{15} (- 4 \frac{x}{362797056})^{2} + \frac{17 !}{3 ! ( 17 - 3 ) !} \cdot 6^{14} (- 4 \frac{x}{362797056})^{3} + \frac{17 !}{4 ! ( 17 - 4 ) !} \cdot 6^{13} (- 4 \frac{x}{362797056})^{4} + \frac{17 !}{5 ! ( 17 - 5 ) !} \cdot 6^{12} (- 4 \frac{x}{362797056})^{5} + \frac{17 !}{6 ! ( 17 - 6 ) !} \cdot 6^{11} (- 4 \frac{x}{362797056})^{6} + \frac{17 !}{7 ! ( 17 - 7 ) !} \cdot 6^{10} (- 4 \frac{x}{362797056})^{7} + \frac{17 !}{8 ! ( 17 - 8 ) !} \cdot 6^{9} (- 4 \frac{x}{362797056})^{8} + \frac{17 !}{9 ! ( 17 - 9 ) !} \cdot 6^{8} (- 4 \frac{x}{362797056})^{9} + \frac{17 !}{10 ! ( 17 - 10 ) !} \cdot 6^{7} (- 4 \frac{x}{362797056})^{10} + \frac{17 !}{11 ! ( 17 - 11 ) !} \cdot 6^{6} (- 4 \frac{x}{362797056})^{11} + \frac{17 !}{12 ! ( 17 - 12 ) !} \cdot 6^{5} (- 4 \frac{x}{362797056})^{12} + \frac{17 !}{13 ! ( 17 - 13 ) !} \cdot 6^{4} (- 4 \frac{x}{362797056})^{13} + \frac{17 !}{14 ! ( 17 - 14 ) !} \cdot 6^{3} (- 4 \frac{x}{362797056})^{14} + \frac{17 !}{15 ! ( 17 - 15 ) !} \cdot 6^{2} (- 4 \frac{x}{362797056})^{15} + \frac{17 !}{16 ! ( 17 - 16 ) !} \cdot 6^{1} (- 4 \frac{x}{362797056})^{16} + \frac{17 !}{17 ! ( 17 - 17 ) !} \cdot 6^{0} (- 4 \frac{x}{362797056})^{17}

Simplificar

\frac{17 !}{0 ! ( 17 - 0 ) !} \cdot 6^{17} (- 4 \frac{x}{362797056})^{0} : 6^{17}

Simplificar

\frac{17 !}{1 ! ( 17 - 1 ) !} \cdot 6^{16} (- 4 \frac{x}{362797056})^{1} : - \frac{6 ^{16} \cdot 17 4 x}{4 362797056}

Simplificar

\frac{17 !}{2 ! ( 17 - 2 ) !} \cdot 6^{15} (- 4 \frac{x}{362797056})^{2} : 6^{15} \cdot 136 (4 \frac{x}{362797056})^{2}

Simplificar

\frac{17 !}{3 ! ( 17 - 3 ) !} \cdot 6^{14} (- 4 \frac{x}{362797056})^{3} : - 6^{14} \cdot 680 (4 \frac{x}{362797056})^{3}

Simplificar

\frac{17 !}{4 ! ( 17 - 4 ) !} \cdot 6^{13} (- 4 \frac{x}{362797056})^{4} : 85680 x

Simplificar

\frac{17 !}{5 ! ( 17 - 5 ) !} \cdot 6^{12} (- 4 \frac{x}{362797056})^{5} : - 6^{12} \cdot 6188 (4 \frac{x}{362797056})^{5}

Simplificar

\frac{17 !}{6 ! ( 17 - 6 ) !} \cdot 6^{11} (- 4 \frac{x}{362797056})^{6} : 4489976365056 (4 \frac{x}{362797056})^{6}

Simplificar

\frac{17 !}{7 ! ( 17 - 7 ) !} \cdot 6^{10} (- 4 \frac{x}{362797056})^{7} : - 1175946190848 (4 \frac{x}{362797056})^{7}

Simplificar

\frac{17 !}{8 ! ( 17 - 8 ) !} \cdot 6^{9} (- 4 \frac{x}{362797056})^{8} : \frac{244988789760 x ^{2}}{36279705 6 ^{2}}

Simplificar

\frac{17 !}{9 ! ( 17 - 9 ) !} \cdot 6^{8} (- 4 \frac{x}{362797056})^{9} : - 40831464960 (4 \frac{x}{362797056})^{9}

Simplificar

\frac{17 !}{10 ! ( 17 - 10 ) !} \cdot 6^{7} (- 4 \frac{x}{362797056})^{10} : 5444195328 (4 \frac{x}{362797056})^{10}

Simplificar

\frac{17 !}{11 ! ( 17 - 11 ) !} \cdot 6^{6} (- 4 \frac{x}{362797056})^{11} : - 577414656 (4 \frac{x}{362797056})^{11}

Simplificar

\frac{17 !}{12 ! ( 17 - 12 ) !} \cdot 6^{5} (- 4 \frac{x}{362797056})^{12} : \frac{48117888 x ^{3}}{36279705 6 ^{3}}

Simplificar

\frac{17 !}{13 ! ( 17 - 13 ) !} \cdot 6^{4} (- 4 \frac{x}{362797056})^{13} : - 3084480 (4 \frac{x}{362797056})^{13}

Simplificar

\frac{17 !}{14 ! ( 17 - 14 ) !} \cdot 6^{3} (- 4 \frac{x}{362797056})^{14} : 146880 (4 \frac{x}{362797056})^{14}

Simplificar

\frac{17 !}{15 ! ( 17 - 15 ) !} \cdot 6^{2} (- 4 \frac{x}{362797056})^{15} : - 4896 (4 \frac{x}{362797056})^{15}

Simplificar

\frac{17 !}{16 ! ( 17 - 16 ) !} \cdot 6^{1} (- 4 \frac{x}{362797056})^{16} : \frac{102 x ^{4}}{36279705 6 ^{4}}

Simplificar

\frac{17 !}{17 ! ( 17 - 17 ) !} \cdot 6^{0} (- 4 \frac{x}{362797056})^{17} : - (4 \frac{x}{362797056})^{17}

= 6^{17} - \frac{6 ^{16} \cdot 17 4 x}{4 362797056} + 6^{15} \cdot 136 (4 \frac{x}{362797056})^{2} - 6^{14} \cdot 680 (4 \frac{x}{362797056})^{3} + 85680 x - 6^{12} \cdot 6188 (4 \frac{x}{362797056})^{5} + 4489976365056 (4 \frac{x}{362797056})^{6} - 1175946190848 (4 \frac{x}{362797056})^{7} + \frac{244988789760 x ^{2}}{36279705 6 ^{2}} - 40831464960 (4 \frac{x}{362797056})^{9} + 5444195328 (4 \frac{x}{362797056})^{10} - 577414656 (4 \frac{x}{362797056})^{11} + \frac{48117888 x ^{3}}{36279705 6 ^{3}} - 3084480 (4 \frac{x}{362797056})^{13} + 146880 (4 \frac{x}{362797056})^{14} - 4896 (4 \frac{x}{362797056})^{15} + \frac{102 x ^{4}}{36279705 6 ^{4}} - (4 \frac{x}{362797056})^{17}

Simplificar

6^{17} - \frac{6 ^{16} \cdot 17 4 x}{4 362797056} + 6^{15} \cdot 136 (4 \frac{x}{362797056})^{2} - 6^{14} \cdot 680 (4 \frac{x}{362797056})^{3} + 85680 x - 6^{12} \cdot 6188 (4 \frac{x}{362797056})^{5} + 4489976365056 (4 \frac{x}{362797056})^{6} - 1175946190848 (4 \frac{x}{362797056})^{7} + \frac{244988789760 x ^{2}}{36279705 6 ^{2}} - 40831464960 (4 \frac{x}{362797056})^{9} + 5444195328 (4 \frac{x}{362797056})^{10} - 577414656 (4 \frac{x}{362797056})^{11} + \frac{48117888 x ^{3}}{36279705 6 ^{3}} - 3084480 (4 \frac{x}{362797056})^{13} + 146880 (4 \frac{x}{362797056})^{14} - 4896 (4 \frac{x}{362797056})^{15} + \frac{102 x ^{4}}{36279705 6 ^{4}} - (4 \frac{x}{362797056})^{17} : 6^{17} - 6^{13} \cdot 1746 4 x + 6^{15} \cdot 136 (4 \frac{x}{362797056})^{2} - 6^{14} \cdot 680 (4 \frac{x}{362797056})^{3} + 85680 x - 37128 x 4 \frac{x}{362797056} + \frac{1547 x x}{972 6} - \frac{9724 x 4 x ^{3}}{3 4 36279705 6 ^{3}} + \frac{12155 x ^{2}}{6530347008} - \frac{12155 x ^{2} 4 \frac{x}{362797056}}{39182082048} + \frac{2431 x ^{2} x}{58773123072 362797056} - \frac{1547 x ^{2} 4 x ^{3}}{373248 \cdot 97 2 ^{2} 4 36279705 6 ^{3}} + \frac{1547 x ^{3}}{3 ^{28} \cdot 67108864} - \frac{595 x ^{3} 4 \frac{x}{362797056}}{518 4 ^{2} \cdot 6998 4 ^{3}} + \frac{85 x ^{3} x}{172 8 ^{2} \cdot 20995 2 ^{3} 362797056} - \frac{17 x ^{3} 4 x ^{3}}{28 8 ^{5} \cdot 437 4 ^{3} 4 36279705 6 ^{3}} + \frac{17 x ^{4}}{6 ^{43}} - \frac{x ^{4} 4 \frac{x}{362797056}}{36279705 6 ^{4}}

= 6^{17} - 6^{13} \cdot 1746 4 x + 6^{15} \cdot 136 (4 \frac{x}{362797056})^{2} - 6^{14} \cdot 680 (4 \frac{x}{362797056})^{3} + 85680 x - 37128 x 4 \frac{x}{362797056} + \frac{1547 x x}{972 6} - \frac{9724 x 4 x ^{3}}{3 4 36279705 6 ^{3}} + \frac{12155 x ^{2}}{6530347008} - \frac{12155 x ^{2} 4 \frac{x}{362797056}}{39182082048} + \frac{2431 x ^{2} x}{58773123072 362797056} - \frac{1547 x ^{2} 4 x ^{3}}{373248 \cdot 97 2 ^{2} 4 36279705 6 ^{3}} + \frac{1547 x ^{3}}{3 ^{28} \cdot 67108864} - \frac{595 x ^{3} 4 \frac{x}{362797056}}{518 4 ^{2} \cdot 6998 4 ^{3}} + \frac{85 x ^{3} x}{172 8 ^{2} \cdot 20995 2 ^{3} 362797056} - \frac{17 x ^{3} 4 x ^{3}}{28 8 ^{5} \cdot 437 4 ^{3} 4 36279705 6 ^{3}} + \frac{17 x ^{4}}{6 ^{43}} - \frac{x ^{4} 4 \frac{x}{362797056}}{36279705 6 ^{4}}

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