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Popular Álgebra >

expandir (x-pi)^9

Solução

expandir

(x - π)^{9}

Solução

x^{9} - 9 π x^{8} + 36 π^{2} x^{7} - 84 π^{3} x^{6} + 126 π^{4} x^{5} - 126 π^{5} x^{4} + 84 π^{6} x^{3} - 36 π^{7} x^{2} + 9 π^{8} x - π^{9}

Passos da solução

(x - π)^{9}

Aplicar o teorema do binômio:

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

a = x, b = - π

= i = 0 \sum 9 (i 9) x^{(9 - i)} (- π)^{i}

Expandir a soma

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

Simplificar

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

Simplificar

\frac{9 !}{1 ! ( 9 - 1 ) !} x^{8} (- π)^{1} : - 9 π x^{8}

Simplificar

\frac{9 !}{2 ! ( 9 - 2 ) !} x^{7} (- π)^{2} : 36 π^{2} x^{7}

Simplificar

\frac{9 !}{3 ! ( 9 - 3 ) !} x^{6} (- π)^{3} : - 84 π^{3} x^{6}

Simplificar

\frac{9 !}{4 ! ( 9 - 4 ) !} x^{5} (- π)^{4} : 126 π^{4} x^{5}

Simplificar

\frac{9 !}{5 ! ( 9 - 5 ) !} x^{4} (- π)^{5} : - 126 π^{5} x^{4}

Simplificar

\frac{9 !}{6 ! ( 9 - 6 ) !} x^{3} (- π)^{6} : 84 π^{6} x^{3}

Simplificar

\frac{9 !}{7 ! ( 9 - 7 ) !} x^{2} (- π)^{7} : - 36 π^{7} x^{2}

Simplificar

\frac{9 !}{8 ! ( 9 - 8 ) !} x^{1} (- π)^{8} : 9 π^{8} x

\frac{9 !}{9 ! ( 9 - 9 ) !} x^{0} (- π)^{9} = - π^{9}

= x^{9} - 9 π x^{8} + 36 π^{2} x^{7} - 84 π^{3} x^{6} + 126 π^{4} x^{5} - 126 π^{5} x^{4} + 84 π^{6} x^{3} - 36 π^{7} x^{2} + 9 π^{8} x - π^{9}

Exemplos populares

expandir xydx-(x^2+2y^2)dy

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expandir (x-pi)^8

e x p an d (x - π)^{8}

expandir (x-pi)^6

e x p an d (x - π)^{6}

expandir (x(x-1))/(20)

e x p an d \frac{x ( x - 1 )}{20}

expandir ((9x-2)^3)/7

e x p an d \frac{( 9 x - 2 ) ^{3}}{7}