erweitern (x^2+x+1)^5

Lösung

erweitern

(x^{2} + x + 1)^{5}

x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

Schritte zur Lösung

(x^{2} + x + 1)^{5}

(x^{2} + x + 1)^{5} = (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1)

= (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1)

Multipliziere aus

(x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) (x^{2} + x + 1) : x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

= x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

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

e x p an d \frac{( 1 + x ^{2} - x ^{3} ) ( 1 - x ^{2} + x ^{3} )}{1 - x ^{2} - x ^{3}}

e x p an d \frac{8}{( x ^{2} + 4 ) ( x ^{2} + 6 x + 25 )}

e x p an d \frac{1}{4} ((s + 2)^{2} (s - 2)^{3} (s^{2} + 4))

e x p an d 10 - 10 e^{- 3 x} (cos (3 x) + sin (3 x))