erweitern (x^3+x^2+1)^5

Lösung

erweitern

(x^{3} + x^{2} + 1)^{5}

x^{15} + 5 x^{14} + 10 x^{13} + 15 x^{12} + 25 x^{11} + 31 x^{10} + 30 x^{9} + 35 x^{8} + 30 x^{7} + 20 x^{6} + 20 x^{5} + 10 x^{4} + 5 x^{3} + 5 x^{2} + 1

Schritte zur Lösung

(x^{3} + x^{2} + 1)^{5}

(x^{3} + x^{2} + 1)^{5} = (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1)

= (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1)

Multipliziere aus

(x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) (x^{3} + x^{2} + 1) : x^{15} + 5 x^{14} + 10 x^{13} + 15 x^{12} + 25 x^{11} + 31 x^{10} + 30 x^{9} + 35 x^{8} + 30 x^{7} + 20 x^{6} + 20 x^{5} + 10 x^{4} + 5 x^{3} + 5 x^{2} + 1

= x^{15} + 5 x^{14} + 10 x^{13} + 15 x^{12} + 25 x^{11} + 31 x^{10} + 30 x^{9} + 35 x^{8} + 30 x^{7} + 20 x^{6} + 20 x^{5} + 10 x^{4} + 5 x^{3} + 5 x^{2} + 1

e x p an d e^{2} x (e^{4} x - 4 e^{2 x})

e x p an d A (14, - 10) B (5, 3)

e x p an d (x) + (x + 1) d x

e x p an d sin (\frac{2 π x}{4 + 4 x})

e x p an d 3 x + x