erweitern ((20d-ta)^2)/(25t^2)

Lösung

erweitern

\frac{( 20 d - t a ) ^{2}}{25 t ^{2}}

\frac{16 d ^{2}}{t ^{2}} - \frac{8 d a}{5 t} + \frac{a ^{2}}{25}

Schritte zur Lösung

\frac{( 20 d - t a ) ^{2}}{25 t ^{2}}

(20 d - t a)^{2} = 400 d^{2} - 40 d t a + t^{2} a^{2}

= \frac{400 d ^{2} - 40 d t a + t ^{2} a ^{2}}{25 t ^{2}}

Wende Bruchregel an:

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

\frac{400 d ^{2} - 40 d t a + t ^{2} a ^{2}}{25 t ^{2}} = \frac{400 d ^{2}}{25 t ^{2}} - \frac{40 d t a}{25 t ^{2}} + \frac{t ^{2} a ^{2}}{25 t ^{2}}

= \frac{400 d ^{2}}{25 t ^{2}} - \frac{40 d t a}{25 t ^{2}} + \frac{t ^{2} a ^{2}}{25 t ^{2}}

Teile die Zahlen:

\frac{400}{25} = 16

= \frac{16 d ^{2}}{t ^{2}} - \frac{40 d t a}{25 t ^{2}} + \frac{t ^{2} a ^{2}}{25 t ^{2}}

Streiche

\frac{40 d t a}{25 t ^{2}} : \frac{8 d a}{5 t}

= \frac{16 d ^{2}}{t ^{2}} - \frac{8 d a}{5 t} + \frac{t ^{2} a ^{2}}{25 t ^{2}}

Streiche

\frac{t ^{2} a ^{2}}{25 t ^{2}} : \frac{a ^{2}}{25}

= \frac{16 d ^{2}}{t ^{2}} - \frac{8 d a}{5 t} + \frac{a ^{2}}{25}

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