erweitern (h(x+a)^2-h(x))/a

Lösung

erweitern

\frac{h ( x + a ) ^{2} - h ( x )}{a}

\frac{h x ^{2}}{a} + 2 h x + ah - \frac{h x}{a}

Schritte zur Lösung

\frac{h ( x + a ) ^{2} - h ( x )}{a}

Entferne die Klammern:

(a) = a

= \frac{h ( x + a ) ^{2} - h x}{a}

(x + a)^{2} = x^{2} + 2 a x + a^{2}

= \frac{h ( x ^{2} + 2 a x + a ^{2} ) - h x}{a}

Multipliziere aus

h (x^{2} + 2 x a + a^{2}) - h x : h x^{2} + 2 ah x + a^{2} h - h x

= \frac{h x ^{2} + 2 ah x + a ^{2} h - h x}{a}

Wende Bruchregel an:

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

\frac{h x ^{2} + 2 ah x + a ^{2} h - h x}{a} = \frac{h x ^{2}}{a} + \frac{2 ah x}{a} + \frac{a ^{2} h}{a} - \frac{h x}{a}

= \frac{h x ^{2}}{a} + \frac{2 ah x}{a} + \frac{a ^{2} h}{a} - \frac{h x}{a}

Streiche

\frac{2 ah x}{a} : 2 h x

= \frac{h x ^{2}}{a} + 2 h x + \frac{a ^{2} h}{a} - \frac{h x}{a}

Streiche

\frac{a ^{2} h}{a} : ah

= \frac{h x ^{2}}{a} + 2 h x + ah - \frac{h x}{a}

e x p an d \frac{3 u + 2}{6 ( u + 2 )}

e x p an d 7^{^{'}} (5 x + 1) - 10 x

s im pl i f y e^{- i θ} (1 + e^{i θ} + e^{2 i θ})

e x p an d \frac{2 t + 1}{2 ( t ^{2} + t )}

e x p an d a (- 5, - 1) b (- 1, 1)