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Popular Álgebra >

desarrollar (x-3)^{14}

Solución

desarrollar

(x - 3)^{14}

Solución

x^{14} - 42 x^{13} + 819 x^{12} - 9828 x^{11} + 81081 x^{10} - 486486 x^{9} + 2189187 x^{8} - 7505784 x^{7} + 19702683 x^{6} - 39405366 x^{5} + 59108049 x^{4} - 64481508 x^{3} + 48361131 x^{2} - 22320522 x + 4782969

Pasos de solución

(x - 3)^{14}

Aplicar el teorema del binomio:

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

a = x, b = - 3

= i = 0 \sum 14 (i 14) x^{(14 - i)} (- 3)^{i}

Expandir sumatorio

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

Simplificar

\frac{14 !}{0 ! ( 14 - 0 ) !} x^{14} (- 3)^{0} : x^{14}

Simplificar

\frac{14 !}{1 ! ( 14 - 1 ) !} x^{13} (- 3)^{1} : - 42 x^{13}

Simplificar

\frac{14 !}{2 ! ( 14 - 2 ) !} x^{12} (- 3)^{2} : 819 x^{12}

Simplificar

\frac{14 !}{3 ! ( 14 - 3 ) !} x^{11} (- 3)^{3} : - 9828 x^{11}

Simplificar

\frac{14 !}{4 ! ( 14 - 4 ) !} x^{10} (- 3)^{4} : 81081 x^{10}

Simplificar

\frac{14 !}{5 ! ( 14 - 5 ) !} x^{9} (- 3)^{5} : - 486486 x^{9}

Simplificar

\frac{14 !}{6 ! ( 14 - 6 ) !} x^{8} (- 3)^{6} : 2189187 x^{8}

Simplificar

\frac{14 !}{7 ! ( 14 - 7 ) !} x^{7} (- 3)^{7} : - 7505784 x^{7}

Simplificar

\frac{14 !}{8 ! ( 14 - 8 ) !} x^{6} (- 3)^{8} : 19702683 x^{6}

Simplificar

\frac{14 !}{9 ! ( 14 - 9 ) !} x^{5} (- 3)^{9} : - 39405366 x^{5}

Simplificar

\frac{14 !}{10 ! ( 14 - 10 ) !} x^{4} (- 3)^{10} : 59108049 x^{4}

Simplificar

\frac{14 !}{11 ! ( 14 - 11 ) !} x^{3} (- 3)^{11} : - 64481508 x^{3}

Simplificar

\frac{14 !}{12 ! ( 14 - 12 ) !} x^{2} (- 3)^{12} : 48361131 x^{2}

Simplificar

\frac{14 !}{13 ! ( 14 - 13 ) !} x^{1} (- 3)^{13} : - 22320522 x

Simplificar

\frac{14 !}{14 ! ( 14 - 14 ) !} x^{0} (- 3)^{14} : 4782969

= x^{14} - 42 x^{13} + 819 x^{12} - 9828 x^{11} + 81081 x^{10} - 486486 x^{9} + 2189187 x^{8} - 7505784 x^{7} + 19702683 x^{6} - 39405366 x^{5} + 59108049 x^{4} - 64481508 x^{3} + 48361131 x^{2} - 22320522 x + 4782969

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