erweitern (x-pi/2)^3

Lösung

erweitern

(x - \frac{π}{2})^{3}

x^{3} - \frac{3 π x ^{2}}{2} + \frac{3 π ^{2} x}{4} - \frac{π ^{3}}{8}

Schritte zur Lösung

(x - \frac{π}{2})^{3}

Wende Formel für perfekte dritte Potenzen an:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = x, b = \frac{π}{2}

= x^{3} - 3 x^{2} \frac{π}{2} + 3 x (\frac{π}{2})^{2} - (\frac{π}{2})^{3}

Vereinfache

x^{3} - 3 x^{2} \frac{π}{2} + 3 x (\frac{π}{2})^{2} - (\frac{π}{2})^{3} : x^{3} - \frac{3 π x ^{2}}{2} + \frac{3 π ^{2} x}{4} - \frac{π ^{3}}{8}

= x^{3} - \frac{3 π x ^{2}}{2} + \frac{3 π ^{2} x}{4} - \frac{π ^{3}}{8}

s im pl i f y (3 - 2 x)^{2}

s im pl i f y (5 c + \frac{2}{3}) (5 c - \frac{2}{3})

e x p an d \frac{( x - 5 ) ( x + 2 )}{x + 1}

e x p an d (2 + cos (θ))^{2}

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