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

Lösung

erweitern

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

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

Schritte zur Lösung

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

(x + 1)^{4} = x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1

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

Wende Bruchregel an:

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

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

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

Teile die Zahlen:

\frac{4}{4} = 1

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

Streiche

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

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

Teile die Zahlen:

\frac{4}{4} = 1

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

e x p an d lo g_{2} (4 w z)

e x p an d \frac{x ^{2} - 3}{( s + 2 ) ( x ^{2} + 2 x + 1 )}

e x p an d (\frac{3}{x})^{1 + 4 x} (4 ln (\frac{3}{x}) - \frac{1 + 4 x}{x})

e x p an d (t - 3) H (t - 1)

e x p an d \frac{- 2 x ^{2} + 3 x - 24}{( x ^{2} + 9 ) ( x - 2 )}