expandir (x-pi)^6

Solução

expandir

(x - π)^{6}

x^{6} - 6 π x^{5} + 15 π^{2} x^{4} - 20 π^{3} x^{3} + 15 π^{4} x^{2} - 6 π^{5} x + π^{6}

Passos da solução

(x - π)^{6}

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 6 (i 6) x^{(6 - i)} (- π)^{i}

Expandir a soma

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

Simplificar

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- π)^{0} : x^{6}

Simplificar

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} (- π)^{1} : - 6 π x^{5}

Simplificar

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- π)^{2} : 15 π^{2} x^{4}

Simplificar

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- π)^{3} : - 20 π^{3} x^{3}

Simplificar

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- π)^{4} : 15 π^{4} x^{2}

Simplificar

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- π)^{5} : - 6 π^{5} x

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- π)^{6} = π^{6}

= x^{6} - 6 π x^{5} + 15 π^{2} x^{4} - 20 π^{3} x^{3} + 15 π^{4} x^{2} - 6 π^{5} x + π^{6}

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

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

e x p an d \frac{1}{v ( m - 3 )}

e x p an d - 2 (2 z + 1 = 26)

e x p an d \frac{b}{x ( x + a )}