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Popular Álgebra >

expandir (x-3)^{10}

Solução

expandir

(x - 3)^{10}

Solução

x^{10} - 30 x^{9} + 405 x^{8} - 3240 x^{7} + 17010 x^{6} - 61236 x^{5} + 153090 x^{4} - 262440 x^{3} + 295245 x^{2} - 196830 x + 59049

Passos da solução

(x - 3)^{10}

Aplicar o teorema do binômio:

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

a = x, b = - 3

= i = 0 \sum 10 (i 10) x^{(10 - i)} (- 3)^{i}

Expandir a soma

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

Simplificar

\frac{10 !}{0 ! ( 10 - 0 ) !} x^{10} (- 3)^{0} : x^{10}

Simplificar

\frac{10 !}{1 ! ( 10 - 1 ) !} x^{9} (- 3)^{1} : - 30 x^{9}

Simplificar

\frac{10 !}{2 ! ( 10 - 2 ) !} x^{8} (- 3)^{2} : 405 x^{8}

Simplificar

\frac{10 !}{3 ! ( 10 - 3 ) !} x^{7} (- 3)^{3} : - 3240 x^{7}

Simplificar

\frac{10 !}{4 ! ( 10 - 4 ) !} x^{6} (- 3)^{4} : 17010 x^{6}

Simplificar

\frac{10 !}{5 ! ( 10 - 5 ) !} x^{5} (- 3)^{5} : - 61236 x^{5}

Simplificar

\frac{10 !}{6 ! ( 10 - 6 ) !} x^{4} (- 3)^{6} : 153090 x^{4}

Simplificar

\frac{10 !}{7 ! ( 10 - 7 ) !} x^{3} (- 3)^{7} : - 262440 x^{3}

Simplificar

\frac{10 !}{8 ! ( 10 - 8 ) !} x^{2} (- 3)^{8} : 295245 x^{2}

Simplificar

\frac{10 !}{9 ! ( 10 - 9 ) !} x^{1} (- 3)^{9} : - 196830 x

Simplificar

\frac{10 !}{10 ! ( 10 - 10 ) !} x^{0} (- 3)^{10} : 59049

= x^{10} - 30 x^{9} + 405 x^{8} - 3240 x^{7} + 17010 x^{6} - 61236 x^{5} + 153090 x^{4} - 262440 x^{3} + 295245 x^{2} - 196830 x + 59049

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