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

Lösung

erweitern

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

x^{10} - 25 x^{9} + 255 x^{8} - 1350 x^{7} + 3885 x^{6} - 5775 x^{5} + 3885 x^{4} - 1350 x^{3} + 255 x^{2} - 25 x + 1

Schritte zur Lösung

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

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

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

Multipliziere aus

(x^{2} - 5 x + 1) (x^{2} - 5 x + 1) (x^{2} - 5 x + 1) (x^{2} - 5 x + 1) (x^{2} - 5 x + 1) : x^{10} - 25 x^{9} + 255 x^{8} - 1350 x^{7} + 3885 x^{6} - 5775 x^{5} + 3885 x^{4} - 1350 x^{3} + 255 x^{2} - 25 x + 1

= x^{10} - 25 x^{9} + 255 x^{8} - 1350 x^{7} + 3885 x^{6} - 5775 x^{5} + 3885 x^{4} - 1350 x^{3} + 255 x^{2} - 25 x + 1

e x p an d (x + 9) l e f t (x - 3)

e x p an d \frac{5 t ^{2} + 21 t + 10}{2 t ( t + 5 ) ( t + 2 )}

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

s im pl i f y t (x) x^{^{''}} + (4 t (x) - 2) x^{^{'}} + 4 x

\frac{d}{d y} ((x) (2 x + 1))