erweitern ((x^4+1)^3)/(x^6)

Lösung

erweitern

\frac{( x ^{4} + 1 ) ^{3}}{x ^{6}}

x^{6} + 3 x^{2} + \frac{3}{x ^{2}} + \frac{1}{x ^{6}}

Schritte zur Lösung

\frac{( x ^{4} + 1 ) ^{3}}{x ^{6}}

(x^{4} + 1)^{3} = x^{12} + 3 x^{8} + 3 x^{4} + 1

= \frac{x ^{12} + 3 x ^{8} + 3 x ^{4} + 1}{x ^{6}}

Wende Bruchregel an:

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

\frac{x ^{12} + 3 x ^{8} + 3 x ^{4} + 1}{x ^{6}} = \frac{x ^{12}}{x ^{6}} + \frac{3 x ^{8}}{x ^{6}} + \frac{3 x ^{4}}{x ^{6}} + \frac{1}{x ^{6}}

= \frac{x ^{12}}{x ^{6}} + \frac{3 x ^{8}}{x ^{6}} + \frac{3 x ^{4}}{x ^{6}} + \frac{1}{x ^{6}}

Streiche

\frac{x ^{12}}{x ^{6}} : x^{6}

= x^{6} + \frac{3 x ^{8}}{x ^{6}} + \frac{3 x ^{4}}{x ^{6}} + \frac{1}{x ^{6}}

Streiche

\frac{3 x ^{8}}{x ^{6}} : 3 x^{2}

= x^{6} + 3 x^{2} + \frac{3 x ^{4}}{x ^{6}} + \frac{1}{x ^{6}}

Streiche

\frac{3 x ^{4}}{x ^{6}} : \frac{3}{x ^{2}}

= x^{6} + 3 x^{2} + \frac{3}{x ^{2}} + \frac{1}{x ^{6}}

e x p an d - 3 π (3 \cdot 2^{\frac{1}{2}} - 5)

e x p an d (t - e^{2 t}) (3 + 2 e^{2 t})

e x p an d (2 t + 3) \cdot (ln (2 t - 3))

e x p an d 4 (x - 1) - 2 (3 x + 5 = - 3 x - 1)

e x p an d e^{P} (P + P P)