erweitern ((2a-3b)^2)/(36)

Lösung

erweitern

\frac{( 2 a - 3 b ) ^{2}}{36}

\frac{a ^{2}}{9} - \frac{ab}{3} + \frac{b ^{2}}{4}

Schritte zur Lösung

\frac{( 2 a - 3 b ) ^{2}}{36}

(2 a - 3 b)^{2} = 4 a^{2} - 12 ab + 9 b^{2}

= \frac{4 a ^{2} - 12 ab + 9 b ^{2}}{36}

Wende Bruchregel an:

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

\frac{4 a ^{2} - 12 ab + 9 b ^{2}}{36} = \frac{4 a ^{2}}{36} - \frac{12 ab}{36} + \frac{9 b ^{2}}{36}

= \frac{4 a ^{2}}{36} - \frac{12 ab}{36} + \frac{9 b ^{2}}{36}

Streiche

\frac{4 a ^{2}}{36} : \frac{a ^{2}}{9}

= \frac{a ^{2}}{9} - \frac{12 ab}{36} + \frac{9 b ^{2}}{36}

Streiche

\frac{12 ab}{36} : \frac{ab}{3}

= \frac{a ^{2}}{9} - \frac{ab}{3} + \frac{9 b ^{2}}{36}

Streiche

\frac{9 b ^{2}}{36} : \frac{b ^{2}}{4}

= \frac{a ^{2}}{9} - \frac{ab}{3} + \frac{b ^{2}}{4}

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