erweitern (a^2+b^2)^3

Lösung

erweitern

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

a^{6} + 3 a^{4} b^{2} + 3 a^{2} b^{4} + b^{6}

Schritte zur Lösung

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

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

Vereinfache

(a^{2})^{3} + 3 (a^{2})^{2} b^{2} + 3 a^{2} (b^{2})^{2} + (b^{2})^{3} : a^{6} + 3 a^{4} b^{2} + 3 a^{2} b^{4} + b^{6}

= a^{6} + 3 a^{4} b^{2} + 3 a^{2} b^{4} + b^{6}

s im pl i f y \frac{3 48}{3 3}

s im pl i f y (22 + 3)^{2}

s im pl i f y 8^{2} + 1 2^{2}

f a c t or 16 m^{2} n + 24 mn - 40 m n^{2}

s im pl i f y \frac{x ^{3} - 8}{x ^{2} + 2 x + 4}