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Popular Álgebra >

desarrollar (x+3)^9

Solución

desarrollar

(x + 3)^{9}

Solución

x^{9} + 27 x^{8} + 324 x^{7} + 2268 x^{6} + 10206 x^{5} + 30618 x^{4} + 61236 x^{3} + 78732 x^{2} + 59049 x + 19683

Pasos de solución

(x + 3)^{9}

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 9 (i 9) x^{(9 - i)} \cdot 3^{i}

Expandir sumatorio

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

Simplificar

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

Simplificar

\frac{9 !}{1 ! ( 9 - 1 ) !} x^{8} \cdot 3^{1} : 27 x^{8}

Simplificar

\frac{9 !}{2 ! ( 9 - 2 ) !} x^{7} \cdot 3^{2} : 324 x^{7}

Simplificar

\frac{9 !}{3 ! ( 9 - 3 ) !} x^{6} \cdot 3^{3} : 2268 x^{6}

Simplificar

\frac{9 !}{4 ! ( 9 - 4 ) !} x^{5} \cdot 3^{4} : 10206 x^{5}

Simplificar

\frac{9 !}{5 ! ( 9 - 5 ) !} x^{4} \cdot 3^{5} : 30618 x^{4}

Simplificar

\frac{9 !}{6 ! ( 9 - 6 ) !} x^{3} \cdot 3^{6} : 61236 x^{3}

Simplificar

\frac{9 !}{7 ! ( 9 - 7 ) !} x^{2} \cdot 3^{7} : 78732 x^{2}

Simplificar

\frac{9 !}{8 ! ( 9 - 8 ) !} x^{1} \cdot 3^{8} : 59049 x

Simplificar

\frac{9 !}{9 ! ( 9 - 9 ) !} x^{0} \cdot 3^{9} : 19683

= x^{9} + 27 x^{8} + 324 x^{7} + 2268 x^{6} + 10206 x^{5} + 30618 x^{4} + 61236 x^{3} + 78732 x^{2} + 59049 x + 19683

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