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Popular Álgebra >

expandir (2x+3)^9

Solução

expandir

(2 x + 3)^{9}

Solução

512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683

Passos da solução

(2 x + 3)^{9}

Aplicar o teorema do binômio:

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

a = 2 x, b = 3

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

Expandir a soma

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

Simplificar

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

Simplificar

\frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} \cdot 3^{1} : 6912 x^{8}

Simplificar

\frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} \cdot 3^{2} : 41472 x^{7}

Simplificar

\frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} \cdot 3^{3} : 145152 x^{6}

Simplificar

\frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} \cdot 3^{4} : 326592 x^{5}

Simplificar

\frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} \cdot 3^{5} : 489888 x^{4}

Simplificar

\frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} \cdot 3^{6} : 489888 x^{3}

Simplificar

\frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} \cdot 3^{7} : 314928 x^{2}

Simplificar

\frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} \cdot 3^{8} : 118098 x

Simplificar

\frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} \cdot 3^{9} : 19683

= 512 x^{9} + 6912 x^{8} + 41472 x^{7} + 145152 x^{6} + 326592 x^{5} + 489888 x^{4} + 489888 x^{3} + 314928 x^{2} + 118098 x + 19683

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