erweitern (a+b+c)^3

Lösung

erweitern

(a + b + c)^{3}

a^{3} + 3 a^{2} b + 3 a^{2} c + 3 a c^{2} + 3 b c^{2} + 3 a b^{2} + c^{3} + 3 b^{2} c + 6 ab c + b^{3}

Schritte zur Lösung

(a + b + c)^{3}

Vereinfache

(a + b + c)^{3} : (a + b + c) (a + b + c) (a + b + c)

= (a + b + c) (a + b + c) (a + b + c)

Schreibe

(a + b + c) (a + b + c)

um:

a^{2} + 2 ab + 2 a c + b^{2} + 2 b c + c^{2}

= (a^{2} + 2 ab + 2 a c + b^{2} + 2 b c + c^{2}) (a + b + c)

Setze Klammern

= a^{2} a + a^{2} b + a^{2} c + 2 aba + 2 abb + 2 ab c + 2 a c a + 2 a c b + 2 a cc + b^{2} a + b^{2} b + b^{2} c + 2 b c a + 2 b c b + 2 b cc + c^{2} a + c^{2} b + c^{2} c

Vereinfache

a^{2} a + a^{2} b + a^{2} c + 2 aba + 2 abb + 2 ab c + 2 a c a + 2 a c b + 2 a cc + b^{2} a + b^{2} b + b^{2} c + 2 b c a + 2 b c b + 2 b cc + c^{2} a + c^{2} b + c^{2} c : a^{3} + 3 a^{2} b + 3 a^{2} c + 3 a c^{2} + 3 b c^{2} + 3 a b^{2} + c^{3} + 3 b^{2} c + 6 ab c + b^{3}

= a^{3} + 3 a^{2} b + 3 a^{2} c + 3 a c^{2} + 3 b c^{2} + 3 a b^{2} + c^{3} + 3 b^{2} c + 6 ab c + b^{3}

s im pl i f y \frac{5}{15}

s im pl i f y \frac{24}{3}

s im pl i f y \frac{1}{1 - sin ( x )} + \frac{1}{1 + sin ( x )}

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

\frac{17}{2}