erweitern ((3yz-5x)^2)/(225)

Lösung

erweitern

\frac{( 3 yz - 5 x ) ^{2}}{225}

\frac{y ^{2} z ^{2}}{25} - \frac{2 yz x}{15} + \frac{x ^{2}}{9}

Schritte zur Lösung

\frac{( 3 yz - 5 x ) ^{2}}{225}

(3 yz - 5 x)^{2} = 9 y^{2} z^{2} - 30 yz x + 25 x^{2}

= \frac{9 y ^{2} z ^{2} - 30 yz x + 25 x ^{2}}{225}

Wende Bruchregel an:

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

\frac{9 y ^{2} z ^{2} - 30 yz x + 25 x ^{2}}{225} = \frac{9 y ^{2} z ^{2}}{225} - \frac{30 yz x}{225} + \frac{25 x ^{2}}{225}

= \frac{9 y ^{2} z ^{2}}{225} - \frac{30 yz x}{225} + \frac{25 x ^{2}}{225}

Streiche

\frac{9 y ^{2} z ^{2}}{225} : \frac{y ^{2} z ^{2}}{25}

= \frac{y ^{2} z ^{2}}{25} - \frac{30 yz x}{225} + \frac{25 x ^{2}}{225}

Streiche

\frac{30 yz x}{225} : \frac{2 yz x}{15}

= \frac{y ^{2} z ^{2}}{25} - \frac{2 yz x}{15} + \frac{25 x ^{2}}{225}

Streiche

\frac{25 x ^{2}}{225} : \frac{x ^{2}}{9}

= \frac{y ^{2} z ^{2}}{25} - \frac{2 yz x}{15} + \frac{x ^{2}}{9}

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