erweitern ((yy-2y+1)/4)^2

Lösung

erweitern

(\frac{yy - 2 y + 1}{4})^{2}

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

Schritte zur Lösung

(\frac{yy - 2 y + 1}{4})^{2}

\frac{yy - 2 y + 1}{4} = \frac{y ^{2} - 2 y + 1}{4}

= (\frac{y ^{2} - 2 y + 1}{4})^{2}

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( y ^{2} - 2 y + 1 ) ^{2}}{4 ^{2}}

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

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

4^{2} = 16

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

Streiche

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

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

Streiche

\frac{4 y}{16} : \frac{y}{4}

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

\frac{d}{d y} ((x (y)) (\frac{y ^{6}}{6} + \frac{1}{16 y ^{4}})^{2})

e x p an d \frac{2 ( 2 i z ^{2} - 15 z ^{2} + 15 i z + 16 z - 14 i )}{( z - i ) ^{5}}

e x p an d (\frac{2 x + 1}{4 x}) \cdot (\frac{- 16}{x ( 1 + x ) ( x - 4 ) ^{2}})

e x p an d 2 y (x y^{'} (x) - y)

e x p an d π x^{2} \cdot (9 - x) - 90