erweitern (1+x+3x^2)^6

Lösung

erweitern

(1 + x + 3 x^{2})^{6}

729 x^{12} + 1458 x^{11} + 2673 x^{10} + 2970 x^{9} + 2970 x^{8} + 2178 x^{7} + 1441 x^{6} + 726 x^{5} + 330 x^{4} + 110 x^{3} + 33 x^{2} + 6 x + 1

Schritte zur Lösung

(1 + x + 3 x^{2})^{6}

(1 + x + 3 x^{2})^{6} = (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2})

= (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1)

Multipliziere aus

(1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) : 729 x^{12} + 1458 x^{11} + 2673 x^{10} + 2970 x^{9} + 2970 x^{8} + 2178 x^{7} + 1441 x^{6} + 726 x^{5} + 330 x^{4} + 110 x^{3} + 33 x^{2} + 6 x + 1

= 729 x^{12} + 1458 x^{11} + 2673 x^{10} + 2970 x^{9} + 2970 x^{8} + 2178 x^{7} + 1441 x^{6} + 726 x^{5} + 330 x^{4} + 110 x^{3} + 33 x^{2} + 6 x + 1

e x p an d \frac{y ^{2} ( 2 x - 6 y )}{6 x y ^{2} + 1}

e x p an d (7 x^{2} + 6 y sin (2 x)) d x

e x p an d (sec^{2} (x - 1))^{2}

e x p an d \frac{8 ( e ^{t} - 1 )}{e ^{t} + 20}

e x p an d [(x - 3) (x + 1)] \cdot 6 x - 2