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

Lösung

erweitern

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

- x^{10} + 5 x^{9} - 5 x^{8} - 10 x^{7} + 15 x^{6} + 11 x^{5} - 15 x^{4} - 10 x^{3} + 5 x^{2} + 5 x + 1

Schritte zur Lösung

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

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

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

Multipliziere aus

(x + 1 - x^{2}) (x + 1 - x^{2}) (x + 1 - x^{2}) (x + 1 - x^{2}) (x + 1 - x^{2}) : - x^{10} + 5 x^{9} - 5 x^{8} - 10 x^{7} + 15 x^{6} + 11 x^{5} - 15 x^{4} - 10 x^{3} + 5 x^{2} + 5 x + 1

= - x^{10} + 5 x^{9} - 5 x^{8} - 10 x^{7} + 15 x^{6} + 11 x^{5} - 15 x^{4} - 10 x^{3} + 5 x^{2} + 5 x + 1

e x p an d 1 n (x^{\frac{2}{5}} y^{\frac{4}{3}})

e x p an d \frac{- 3 y ^{3} - 6 x ^{2} y}{x ( 2 x ^{2} + 9 y ^{2} )}

e x p an d \frac{1 - cot ^{4} ( x )}{csc ^{2} ( x ) ( sin ( x ) + cos ( x ) )}

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

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