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

Lösung

erweitern

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

x^{10} - 10 x^{9} + 45 x^{8} - 120 x^{7} + 210 x^{6} - 252 x^{5} + 210 x^{4} - 120 x^{3} + 45 x^{2} - 10 x + 1

Schritte zur Lösung

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

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

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

Multipliziere aus

(1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) (1 - 2 x + x^{2}) : x^{10} - 10 x^{9} + 45 x^{8} - 120 x^{7} + 210 x^{6} - 252 x^{5} + 210 x^{4} - 120 x^{3} + 45 x^{2} - 10 x + 1

= x^{10} - 10 x^{9} + 45 x^{8} - 120 x^{7} + 210 x^{6} - 252 x^{5} + 210 x^{4} - 120 x^{3} + 45 x^{2} - 10 x + 1

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

e x p an d (y^{3} + k x y^{4} - 2 x) d x

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

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

s im pl i f y 1 + \frac{k}{( s + 1 ) ( s ^{2} + s + 1.5 )}