erweitern ((b+a)/2)^2

Lösung

erweitern

(\frac{b + a}{2})^{2}

\frac{b ^{2}}{4} + \frac{ba}{2} + \frac{a ^{2}}{4}

Schritte zur Lösung

(\frac{b + a}{2})^{2}

Wende Exponentenregel an:

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

= \frac{( b + a ) ^{2}}{2 ^{2}}

(b + a)^{2} = b^{2} + 2 ba + a^{2}

= \frac{b ^{2} + 2 ba + a ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{b ^{2} + 2 ba + a ^{2}}{4}

Wende Bruchregel an:

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

\frac{b ^{2} + 2 ba + a ^{2}}{4} = \frac{b ^{2}}{4} + \frac{2 ba}{4} + \frac{a ^{2}}{4}

= \frac{b ^{2}}{4} + \frac{2 ba}{4} + \frac{a ^{2}}{4}

Streiche

\frac{2 ba}{4} : \frac{ba}{2}

= \frac{b ^{2}}{4} + \frac{ba}{2} + \frac{a ^{2}}{4}

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