erweitern-((8xt-wy)^2)/(y^2t^2)

Lösung

erweitern

- \frac{( 8 x t - w y ) ^{2}}{y ^{2} t ^{2}}

- \frac{64 x ^{2}}{y ^{2}} + \frac{16 x w}{t y} - \frac{w ^{2}}{t ^{2}}

Schritte zur Lösung

- \frac{( 8 x t - w y ) ^{2}}{y ^{2} t ^{2}}

(8 x t - w y)^{2} = 64 x^{2} t^{2} - 16 x tw y + w^{2} y^{2}

= - \frac{64 x ^{2} t ^{2} - 16 x tw y + w ^{2} y ^{2}}{t ^{2} y ^{2}}

Wende Bruchregel an:

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

\frac{64 x ^{2} t ^{2} - 16 x tw y + w ^{2} y ^{2}}{y ^{2} t ^{2}} = - (\frac{64 x ^{2} t ^{2}}{y ^{2} t ^{2}}) - (- \frac{16 x tw y}{y ^{2} t ^{2}}) - (\frac{w ^{2} y ^{2}}{y ^{2} t ^{2}})

= - (\frac{64 x ^{2} t ^{2}}{t ^{2} y ^{2}}) - (- \frac{16 x tw y}{t ^{2} y ^{2}}) - (\frac{w ^{2} y ^{2}}{t ^{2} y ^{2}})

Entferne die Klammern:

(a) = a, - (- a) = a

= - \frac{64 x ^{2} t ^{2}}{y ^{2} t ^{2}} + \frac{16 x tw y}{y ^{2} t ^{2}} - \frac{w ^{2} y ^{2}}{y ^{2} t ^{2}}

Streiche

\frac{64 x ^{2} t ^{2}}{y ^{2} t ^{2}} : \frac{64 x ^{2}}{y ^{2}}

= - \frac{64 x ^{2}}{y ^{2}} + \frac{16 x tw y}{t ^{2} y ^{2}} - \frac{w ^{2} y ^{2}}{t ^{2} y ^{2}}

Streiche

\frac{16 x tw y}{y ^{2} t ^{2}} : \frac{16 x w}{t y}

= - \frac{64 x ^{2}}{y ^{2}} + \frac{16 x w}{t y} - \frac{w ^{2} y ^{2}}{t ^{2} y ^{2}}

Streiche

\frac{w ^{2} y ^{2}}{y ^{2} t ^{2}} : \frac{w ^{2}}{t ^{2}}

= - \frac{64 x ^{2}}{y ^{2}} + \frac{16 x w}{t y} - \frac{w ^{2}}{t ^{2}}

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