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Popular Álgebra >

expandir (x-13)^{13}

Solução

expandir

(x - 13)^{13}

Solução

x^{13} - 169 x^{12} + 13182 x^{11} - 628342 x^{10} + 20421115 x^{9} - 477854091 x^{8} + 8282804244 x^{7} - 107676455172 x^{6} + 1049845437927 x^{5} - 1 3^{9} \cdot 715 x^{4} + 1 3^{10} \cdot 286 x^{3} - 1 3^{11} \cdot 78 x^{2} + 1 3^{13} x - 1 3^{13}

Passos da solução

(x - 13)^{13}

Aplicar o teorema do binômio:

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

a = x, b = - 13

= i = 0 \sum 13 (i 13) x^{(13 - i)} (- 13)^{i}

Expandir a soma

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

Simplificar

\frac{13 !}{0 ! ( 13 - 0 ) !} x^{13} (- 13)^{0} : x^{13}

Simplificar

\frac{13 !}{1 ! ( 13 - 1 ) !} x^{12} (- 13)^{1} : - 169 x^{12}

Simplificar

\frac{13 !}{2 ! ( 13 - 2 ) !} x^{11} (- 13)^{2} : 13182 x^{11}

Simplificar

\frac{13 !}{3 ! ( 13 - 3 ) !} x^{10} (- 13)^{3} : - 628342 x^{10}

Simplificar

\frac{13 !}{4 ! ( 13 - 4 ) !} x^{9} (- 13)^{4} : 20421115 x^{9}

Simplificar

\frac{13 !}{5 ! ( 13 - 5 ) !} x^{8} (- 13)^{5} : - 477854091 x^{8}

Simplificar

\frac{13 !}{6 ! ( 13 - 6 ) !} x^{7} (- 13)^{6} : 8282804244 x^{7}

Simplificar

\frac{13 !}{7 ! ( 13 - 7 ) !} x^{6} (- 13)^{7} : - 107676455172 x^{6}

Simplificar

\frac{13 !}{8 ! ( 13 - 8 ) !} x^{5} (- 13)^{8} : 1049845437927 x^{5}

Simplificar

\frac{13 !}{9 ! ( 13 - 9 ) !} x^{4} (- 13)^{9} : - 1 3^{9} \cdot 715 x^{4}

Simplificar

\frac{13 !}{10 ! ( 13 - 10 ) !} x^{3} (- 13)^{10} : 1 3^{10} \cdot 286 x^{3}

Simplificar

\frac{13 !}{11 ! ( 13 - 11 ) !} x^{2} (- 13)^{11} : - 1 3^{11} \cdot 78 x^{2}

Simplificar

\frac{13 !}{12 ! ( 13 - 12 ) !} x^{1} (- 13)^{12} : 1 3^{13} x

Simplificar

\frac{13 !}{13 ! ( 13 - 13 ) !} x^{0} (- 13)^{13} : - 1 3^{13}

= x^{13} - 169 x^{12} + 13182 x^{11} - 628342 x^{10} + 20421115 x^{9} - 477854091 x^{8} + 8282804244 x^{7} - 107676455172 x^{6} + 1049845437927 x^{5} - 1 3^{9} \cdot 715 x^{4} + 1 3^{10} \cdot 286 x^{3} - 1 3^{11} \cdot 78 x^{2} + 1 3^{13} x - 1 3^{13}

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