erweitern ((u-1)/2)^2

Lösung

erweitern

(\frac{u - 1}{2})^{2}

\frac{u ^{2}}{4} - \frac{u}{2} + \frac{1}{4}

Schritte zur Lösung

(\frac{u - 1}{2})^{2}

Wende Exponentenregel an:

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

= \frac{( u - 1 ) ^{2}}{2 ^{2}}

(u - 1)^{2} = u^{2} - 2 u + 1

= \frac{u ^{2} - 2 u + 1}{2 ^{2}}

2^{2} = 4

= \frac{u ^{2} - 2 u + 1}{4}

Wende Bruchregel an:

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

\frac{u ^{2} - 2 u + 1}{4} = \frac{u ^{2}}{4} - \frac{2 u}{4} + \frac{1}{4}

= \frac{u ^{2}}{4} - \frac{2 u}{4} + \frac{1}{4}

Streiche

\frac{2 u}{4} : \frac{u}{2}

= \frac{u ^{2}}{4} - \frac{u}{2} + \frac{1}{4}

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