de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

erweitern (1+z+(z^2)/2)^4

Lösung

erweitern

(1 + z + \frac{z ^{2}}{2})^{4}

Lösung

\frac{17 z ^{4}}{2} + 5 z^{5} + 2 z^{6} + 10 z^{3} + 8 z^{2} + 4 z + 1 + \frac{z ^{7}}{2} + \frac{z ^{8}}{16}

Schritte zur Lösung

(1 + z + \frac{z ^{2}}{2})^{4}

Vereinfache

(1 + z + \frac{z ^{2}}{2})^{4} : (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2})

= (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2})

Schreibe

(1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2})

um:

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

= (1 + 2 z + 2 z^{2} + z^{3} + \frac{z ^{4}}{4}) (1 + z + \frac{z ^{2}}{2}) (1 + z + \frac{z ^{2}}{2})

Schreibe

(1 + 2 z + 2 z^{2} + z^{3} + \frac{z ^{4}}{4}) (1 + z + \frac{z ^{2}}{2})

um:

\frac{9 z ^{4}}{4} + 4 z^{3} + \frac{9 z ^{2}}{2} + 3 z + 1 + \frac{3 z ^{5}}{4} + \frac{z ^{6}}{8}

= (\frac{9 z ^{4}}{4} + 4 z^{3} + \frac{9 z ^{2}}{2} + 3 z + 1 + \frac{3 z ^{5}}{4} + \frac{z ^{6}}{8}) (1 + z + \frac{z ^{2}}{2})

Setze Klammern

= \frac{9 z ^{4}}{4} \cdot 1 + \frac{9 z ^{4}}{4} z + \frac{9 z ^{4}}{4} \cdot \frac{z ^{2}}{2} + 4 z^{3} \cdot 1 + 4 z^{3} z + 4 z^{3} \frac{z ^{2}}{2} + \frac{9 z ^{2}}{2} \cdot 1 + \frac{9 z ^{2}}{2} z + \frac{9 z ^{2}}{2} \cdot \frac{z ^{2}}{2} + 3 z \cdot 1 + 3 zz + 3 z \frac{z ^{2}}{2} + 1 \cdot 1 + 1 \cdot z + 1 \cdot \frac{z ^{2}}{2} + \frac{3 z ^{5}}{4} \cdot 1 + \frac{3 z ^{5}}{4} z + \frac{3 z ^{5}}{4} \cdot \frac{z ^{2}}{2} + \frac{z ^{6}}{8} \cdot 1 + \frac{z ^{6}}{8} z + \frac{z ^{6}}{8} \cdot \frac{z ^{2}}{2}

Vereinfache

\frac{9 z ^{4}}{4} \cdot 1 + \frac{9 z ^{4}}{4} z + \frac{9 z ^{4}}{4} \cdot \frac{z ^{2}}{2} + 4 z^{3} \cdot 1 + 4 z^{3} z + 4 z^{3} \frac{z ^{2}}{2} + \frac{9 z ^{2}}{2} \cdot 1 + \frac{9 z ^{2}}{2} z + \frac{9 z ^{2}}{2} \cdot \frac{z ^{2}}{2} + 3 z \cdot 1 + 3 zz + 3 z \frac{z ^{2}}{2} + 1 \cdot 1 + 1 \cdot z + 1 \cdot \frac{z ^{2}}{2} + \frac{3 z ^{5}}{4} \cdot 1 + \frac{3 z ^{5}}{4} z + \frac{3 z ^{5}}{4} \cdot \frac{z ^{2}}{2} + \frac{z ^{6}}{8} \cdot 1 + \frac{z ^{6}}{8} z + \frac{z ^{6}}{8} \cdot \frac{z ^{2}}{2} : \frac{17 z ^{4}}{2} + 5 z^{5} + 2 z^{6} + 10 z^{3} + 8 z^{2} + 4 z + 1 + \frac{z ^{7}}{2} + \frac{z ^{8}}{16}

= \frac{17 z ^{4}}{2} + 5 z^{5} + 2 z^{6} + 10 z^{3} + 8 z^{2} + 4 z + 1 + \frac{z ^{7}}{2} + \frac{z ^{8}}{16}

Beliebte Beispiele

erweitern sqrt((16u^3+v^3)^2+144u^8v^4+1)

e x p an d (16 u^{3} + v^{3})^{2} + 144 u^{8} v^{4} + 1

erweitern (x-e)(x+y-e)

e x p an d (x - e) (x + y - e)

vereinfachen (x)(sqrt(x+2)+2)

s im pl i f y (x) (x + 2 + 2)

vereinfachen ((sqrt(x)-x^2)(1+sqrt(x)))/(1-x)

s im pl i f y \frac{( x - x ^{2} ) ( 1 + x )}{1 - x}

erweitern (-9,7)y(-9,-1)

e x p an d (- 9, 7) y (- 9, - 1)