erweitern (a+b+c)^5

Lösung

erweitern

(a + b + c)^{5}

a^{5} + 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + b^{5} + c^{5} + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

Schritte zur Lösung

(a + b + c)^{5}

(a + b + c)^{5} = (a + b + c) (a + b + c) (a + b + c) (a + b + c) (a + b + c)

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

Multipliziere aus

(a + b + c) (a + b + c) (a + b + c) (a + b + c) (a + b + c) : a^{5} + 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + b^{5} + c^{5} + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

= a^{5} + 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + b^{5} + c^{5} + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

s im pl i f y (cos (x) + i sin (x))^{4}

s im pl i f y (x - 22) (x + 22)

e x p an d (sin (x) + cos (x) + 1) (sin (x) + cos (x) - 1)

s im pl i f y (i - 1)^{11}

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