erweitern x(1-x-x^3+x^4)^2

Lösung

erweitern

x (1 - x - x^{3} + x^{4})^{2}

x^{9} - 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} + x^{3} - 2 x^{2} + x

Schritte zur Lösung

x (1 - x - x^{3} + x^{4})^{2}

(1 - x - x^{3} + x^{4})^{2} = x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + x^{2} - 2 x + 1

= x (x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + x^{2} - 2 x + 1)

Setze Klammern

= x x^{8} + x (- 2 x^{7}) + x x^{6} + x (- 2 x^{5}) + x \cdot 4 x^{4} + x (- 2 x^{3}) + x x^{2} + x (- 2 x) + x \cdot 1

Wende Minus-Plus Regeln an

+ (- a) = - a

= x^{8} x - 2 x^{7} x + x^{6} x - 2 x^{5} x + 4 x^{4} x - 2 x^{3} x + x^{2} x - 2 xx + 1 \cdot x

Vereinfache

x^{8} x - 2 x^{7} x + x^{6} x - 2 x^{5} x + 4 x^{4} x - 2 x^{3} x + x^{2} x - 2 xx + 1 \cdot x : x^{9} - 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} + x^{3} - 2 x^{2} + x

= x^{9} - 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} + x^{3} - 2 x^{2} + x

e x p an d cos (3 t) U (t - \frac{7 π}{2})

e x p an d V (2, - 3) F (2, - 4)

e x p an d (4 m + 2 n = 70,) (- 3 m + 4 n = 30)

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

e x p an d 3 (403)