erweitern (a^{2x}-sqrt(a))^3

Lösung

erweitern

(a^{2 x} - a)^{3}

a^{6 x} - 3 a^{\frac{8 x + 1}{2}} + 3 a^{2 x + 1} - a a

Schritte zur Lösung

(a^{2 x} - a)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

(a^{2 x})^{3} - 3 (a^{2 x})^{2} a + 3 a^{2 x} (a)^{2} - (a)^{3} : a^{6 x} - 3 a^{\frac{8 x + 1}{2}} + 3 a^{2 x + 1} - a a

= a^{6 x} - 3 a^{\frac{8 x + 1}{2}} + 3 a^{2 x + 1} - a a

e x p an d (5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y

e x p an d (x^{2} + \frac{1}{2 x})^{12}

e x p an d \frac{2 x ^{2} + 4}{( x + 1 ) ( x ^{2} + 5 )}

e x p an d \frac{960 x ^{2} - 132 x + 4.6}{( - 10 x + 1 ) ^{2} ( - 15 x + 1 ) ^{2}}

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