erweitern (1-5/p)^3

Lösung

erweitern

(1 - \frac{5}{p})^{3}

\frac{p ^{3} - 15 p ^{2} - 125 + 75 p}{p ^{3}}

Schritte zur Lösung

(1 - \frac{5}{p})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(1 - \frac{5}{p})^{3} = 1^{3} - 3 \cdot 1^{2} \cdot \frac{5}{p} + 3 \cdot 1 \cdot (\frac{5}{p})^{2} - (\frac{5}{p})^{3}

= 1^{3} - 3 \cdot 1^{2} \cdot \frac{5}{p} + 3 \cdot 1 \cdot (\frac{5}{p})^{2} - (\frac{5}{p})^{3}

Vereinfache

1^{3} - 3 \cdot 1^{2} \cdot \frac{5}{p} + 3 \cdot 1 \cdot (\frac{5}{p})^{2} - (\frac{5}{p})^{3} : \frac{p ^{3} - 15 p ^{2} - 125 + 75 p}{p ^{3}}

= \frac{p ^{3} - 15 p ^{2} - 125 + 75 p}{p ^{3}}

e x p an d - e (- e - e^{2})

e x p an d - \frac{20 s}{( s ^{2} + 25 ) ^{2}}

e x p an d - sec (x) (2 sin (2 x) - tan (x) cos (2 x))

e x p an d \frac{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}{x ^{3}}

e x p an d (\frac{a}{2} - b)^{5}