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Popular Álgebra >

desarrollar (2+x^3)^9

Solución

desarrollar

(2 + x^{3})^{9}

Solución

512 + 2304 x^{3} + 4608 x^{6} + 5376 x^{9} + 4032 x^{12} + 2016 x^{15} + 672 x^{18} + 144 x^{21} + 18 x^{24} + x^{27}

Pasos de solución

(2 + x^{3})^{9}

Aplicar el teorema del binomio:

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

a = 2, b = x^{3}

= i = 0 \sum 9 (i 9) \cdot 2^{(9 - i)} (x^{3})^{i}

Expandir sumatorio

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

Simplificar

\frac{9 !}{0 ! ( 9 - 0 ) !} \cdot 2^{9} (x^{3})^{0} : 512

Simplificar

\frac{9 !}{1 ! ( 9 - 1 ) !} \cdot 2^{8} (x^{3})^{1} : 2304 x^{3}

Simplificar

\frac{9 !}{2 ! ( 9 - 2 ) !} \cdot 2^{7} (x^{3})^{2} : 4608 x^{6}

Simplificar

\frac{9 !}{3 ! ( 9 - 3 ) !} \cdot 2^{6} (x^{3})^{3} : 5376 x^{9}

Simplificar

\frac{9 !}{4 ! ( 9 - 4 ) !} \cdot 2^{5} (x^{3})^{4} : 4032 x^{12}

Simplificar

\frac{9 !}{5 ! ( 9 - 5 ) !} \cdot 2^{4} (x^{3})^{5} : 2016 x^{15}

Simplificar

\frac{9 !}{6 ! ( 9 - 6 ) !} \cdot 2^{3} (x^{3})^{6} : 672 x^{18}

Simplificar

\frac{9 !}{7 ! ( 9 - 7 ) !} \cdot 2^{2} (x^{3})^{7} : 144 x^{21}

Simplificar

\frac{9 !}{8 ! ( 9 - 8 ) !} \cdot 2^{1} (x^{3})^{8} : 18 x^{24}

Simplificar

\frac{9 !}{9 ! ( 9 - 9 ) !} \cdot 2^{0} (x^{3})^{9} : x^{27}

= 512 + 2304 x^{3} + 4608 x^{6} + 5376 x^{9} + 4032 x^{12} + 2016 x^{15} + 672 x^{18} + 144 x^{21} + 18 x^{24} + x^{27}

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