erweitern (x-pi/4)(x-pi/4-h)(x-pi/4-2h)

Lösung

erweitern

(x - \frac{π}{4}) (x - \frac{π}{4} - h) (x - \frac{π}{4} - 2 h)

x^{3} - \frac{3 π x ^{2}}{4} - 3 h x^{2} + \frac{3 π ^{2} x}{16} + 2 h^{2} x + \frac{3 πh x}{2} - \frac{π ^{3}}{64} - \frac{π h ^{2}}{2} - \frac{3 π ^{2} h}{16}

Schritte zur Lösung

(x - \frac{π}{4}) (x - \frac{π}{4} - h) (x - \frac{π}{4} - 2 h)

Multipliziere aus

(x - \frac{π}{4}) (x - \frac{π}{4} - h) : - h x - \frac{π x}{2} + x^{2} + \frac{πh}{4} + \frac{π ^{2}}{16}

= (- h x - \frac{π x}{2} + x^{2} + \frac{πh}{4} + \frac{π ^{2}}{16}) (x - \frac{π}{4} - 2 h)

Multipliziere aus

(- h x - \frac{π x}{2} + x^{2} + \frac{πh}{4} + \frac{π ^{2}}{16}) (x - \frac{π}{4} - 2 h) : x^{3} - \frac{3 π x ^{2}}{4} - 3 h x^{2} + \frac{3 π ^{2} x}{16} + 2 h^{2} x + \frac{3 πh x}{2} - \frac{π ^{3}}{64} - \frac{π h ^{2}}{2} - \frac{3 π ^{2} h}{16}

= x^{3} - \frac{3 π x ^{2}}{4} - 3 h x^{2} + \frac{3 π ^{2} x}{16} + 2 h^{2} x + \frac{3 πh x}{2} - \frac{π ^{3}}{64} - \frac{π h ^{2}}{2} - \frac{3 π ^{2} h}{16}

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