erweitern ((x+1)^4)/(16)

Lösung

erweitern

\frac{( x + 1 ) ^{4}}{16}

\frac{x ^{4}}{16} + \frac{x ^{3}}{4} + \frac{3 x ^{2}}{8} + \frac{x}{4} + \frac{1}{16}

Schritte zur Lösung

\frac{( x + 1 ) ^{4}}{16}

(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}{16}

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}{16} = \frac{x ^{4}}{16} + \frac{4 x ^{3}}{16} + \frac{6 x ^{2}}{16} + \frac{4 x}{16} + \frac{1}{16}

= \frac{x ^{4}}{16} + \frac{4 x ^{3}}{16} + \frac{6 x ^{2}}{16} + \frac{4 x}{16} + \frac{1}{16}

Streiche

\frac{4 x ^{3}}{16} : \frac{x ^{3}}{4}

= \frac{x ^{4}}{16} + \frac{x ^{3}}{4} + \frac{6 x ^{2}}{16} + \frac{4 x}{16} + \frac{1}{16}

Streiche

\frac{6 x ^{2}}{16} : \frac{3 x ^{2}}{8}

= \frac{x ^{4}}{16} + \frac{x ^{3}}{4} + \frac{3 x ^{2}}{8} + \frac{4 x}{16} + \frac{1}{16}

Streiche

\frac{4 x}{16} : \frac{x}{4}

= \frac{x ^{4}}{16} + \frac{x ^{3}}{4} + \frac{3 x ^{2}}{8} + \frac{x}{4} + \frac{1}{16}

e x p an d \frac{13}{( 2 x + 3 ) ( x ^{2} + 1 )}

s im pl i f y x 1 + x \cdot (1 + 1 + x)

e x p an d 39 \cdot 5

e x p an d (tan (t) + 1)^{2}

s im pl i f y x (x + 3)^{2}