expandir ((x-6)^6)/x

Solução

expandir

\frac{( x - 6 ) ^{6}}{x}

x^{5} - 36 x^{4} + 540 x^{3} - 4320 x^{2} + 19440 x - 46656 + \frac{46656}{x}

Passos da solução

\frac{( x - 6 ) ^{6}}{x}

(x - 6)^{6} = x^{6} - 36 x^{5} + 540 x^{4} - 4320 x^{3} + 19440 x^{2} - 46656 x + 46656

= \frac{x ^{6} - 36 x ^{5} + 540 x ^{4} - 4320 x ^{3} + 19440 x ^{2} - 46656 x + 46656}{x}

Aplicar as propriedades das frações:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{6} - 36 x ^{5} + 540 x ^{4} - 4320 x ^{3} + 19440 x ^{2} - 46656 x + 46656}{x} = \frac{x ^{6}}{x} - \frac{36 x ^{5}}{x} + \frac{540 x ^{4}}{x} - \frac{4320 x ^{3}}{x} + \frac{19440 x ^{2}}{x} - \frac{46656 x}{x} + \frac{46656}{x}

= \frac{x ^{6}}{x} - \frac{36 x ^{5}}{x} + \frac{540 x ^{4}}{x} - \frac{4320 x ^{3}}{x} + \frac{19440 x ^{2}}{x} - \frac{46656 x}{x} + \frac{46656}{x}

\frac{x ^{6}}{x} = x^{5}

\frac{36 x ^{5}}{x} = 36 x^{4}

\frac{540 x ^{4}}{x} = 540 x^{3}

\frac{4320 x ^{3}}{x} = 4320 x^{2}

\frac{19440 x ^{2}}{x} = 19440 x

\frac{46656 x}{x} = 46656

= x^{5} - 36 x^{4} + 540 x^{3} - 4320 x^{2} + 19440 x - 46656 + \frac{46656}{x}

so l v e f or f, f = 3 e^{5 x} δ (x - 4)

e x p an d \frac{( a - 1 ) ^{2}}{4}

e x p an d 2 sin (\frac{π}{3}) \cdot cos (\frac{π}{3}) - 1

e x p an d \frac{x ^{2}}{( z - 1 ) ( z + 0.5 )}

e x p an d \frac{( 1 + cos ( x ) ) ^{2} + sin ^{(2)} ( x )}{1 + cos ( x )}