erweitern (5-x^2)^3

Lösung

erweitern

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

125 - 75 x^{2} + 15 x^{4} - x^{6}

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

(5 - x^{2})^{3} = 5^{3} - 3 \cdot 5^{2} x^{2} + 3 \cdot 5 (x^{2})^{2} - (x^{2})^{3}

= 5^{3} - 3 \cdot 5^{2} x^{2} + 3 \cdot 5 (x^{2})^{2} - (x^{2})^{3}

Vereinfache

5^{3} - 3 \cdot 5^{2} x^{2} + 3 \cdot 5 (x^{2})^{2} - (x^{2})^{3} : 125 - 75 x^{2} + 15 x^{4} - x^{6}

= 125 - 75 x^{2} + 15 x^{4} - x^{6}

s im pl i f y \frac{0.7 x ^{3} + 0.7 x ^{3} - 5}{9 x ^{3}}

f a c t or x^{5} + x^{4} - x^{2} - x

s im pl i f y (2 x)^{3} + (3 y)^{3} + (4 z)^{3} - 3 (2 x) (3 y) (4 z)

f a c t or 6 x^{3} + 13 x^{2} + x - 2

f a c t or x^{18} - y^{18}