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

Lösung

erweitern

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

x^{10} - 5 x^{9} + 15 x^{8} - 30 x^{7} + 45 x^{6} - 51 x^{5} + 45 x^{4} - 30 x^{3} + 15 x^{2} - 5 x + 1

Schritte zur Lösung

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

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

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

Multipliziere aus

(1 - x + x^{2}) (1 - x + x^{2}) (1 - x + x^{2}) (1 - x + x^{2}) (1 - x + x^{2}) : x^{10} - 5 x^{9} + 15 x^{8} - 30 x^{7} + 45 x^{6} - 51 x^{5} + 45 x^{4} - 30 x^{3} + 15 x^{2} - 5 x + 1

= x^{10} - 5 x^{9} + 15 x^{8} - 30 x^{7} + 45 x^{6} - 51 x^{5} + 45 x^{4} - 30 x^{3} + 15 x^{2} - 5 x + 1

s im pl i f y (y - 5)^{2}

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

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

e x p an d lo g_{7} (3 \frac{x ^{4} y}{49})

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