erweitern (16(t+h)^2-16t)/h

Lösung

erweitern

\frac{16 ( t + h ) ^{2} - 16 t}{h}

\frac{16 t ^{2}}{h} + 32 t + 16 h - \frac{16 t}{h}

Schritte zur Lösung

\frac{16 ( t + h ) ^{2} - 16 t}{h}

(t + h)^{2} = t^{2} + 2 t h + h^{2}

= \frac{16 ( t ^{2} + 2 t h + h ^{2} ) - 16 t}{h}

Multipliziere aus

16 (t^{2} + 2 t h + h^{2}) - 16 t : 16 t^{2} + 32 t h + 16 h^{2} - 16 t

= \frac{16 t ^{2} + 32 t h + 16 h ^{2} - 16 t}{h}

Wende Bruchregel an:

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

\frac{16 t ^{2} + 32 t h + 16 h ^{2} - 16 t}{h} = \frac{16 t ^{2}}{h} + \frac{32 t h}{h} + \frac{16 h ^{2}}{h} - \frac{16 t}{h}

= \frac{16 t ^{2}}{h} + \frac{32 t h}{h} + \frac{16 h ^{2}}{h} - \frac{16 t}{h}

Streiche

\frac{32 t h}{h} : 32 t

= \frac{16 t ^{2}}{h} + 32 t + \frac{16 h ^{2}}{h} - \frac{16 t}{h}

Streiche

\frac{16 h ^{2}}{h} : 16 h

= \frac{16 t ^{2}}{h} + 32 t + 16 h - \frac{16 t}{h}

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