erweitern (1+x+x^2)^6

Lösung

erweitern

(1 + x + x^{2})^{6}

x^{12} + 6 x^{11} + 21 x^{10} + 50 x^{9} + 90 x^{8} + 126 x^{7} + 141 x^{6} + 126 x^{5} + 90 x^{4} + 50 x^{3} + 21 x^{2} + 6 x + 1

Schritte zur Lösung

(1 + x + x^{2})^{6}

(1 + x + x^{2})^{6} = (1 + x + x^{2}) (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) (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}) (1 + x + x^{2}) : x^{12} + 6 x^{11} + 21 x^{10} + 50 x^{9} + 90 x^{8} + 126 x^{7} + 141 x^{6} + 126 x^{5} + 90 x^{4} + 50 x^{3} + 21 x^{2} + 6 x + 1

= x^{12} + 6 x^{11} + 21 x^{10} + 50 x^{9} + 90 x^{8} + 126 x^{7} + 141 x^{6} + 126 x^{5} + 90 x^{4} + 50 x^{3} + 21 x^{2} + 6 x + 1

e x p an d \frac{( 0.42 - x ) ( x )}{0.14 - x}

e x p an d \frac{( k - 9 ) ( k - 10 )}{k - 4}

e x p an d y^{'} (x) \times (- x^{2} y + 2 x y - y)

e x p an d \frac{1}{( 2 w - 3 ) ^{2}}

e x p an d (6 x^{2} - 8 x^{2} v + v^{2} x^{2}) (v d x + x d v)