erweitern (1+x+x^2)^7

Lösung

erweitern

(1 + x + x^{2})^{7}

x^{14} + 7 x^{13} + 28 x^{12} + 77 x^{11} + 161 x^{10} + 266 x^{9} + 357 x^{8} + 393 x^{7} + 357 x^{6} + 266 x^{5} + 161 x^{4} + 77 x^{3} + 28 x^{2} + 7 x + 1

Schritte zur Lösung

(1 + x + x^{2})^{7}

(1 + x + x^{2})^{7} = (1 + x + x^{2}) (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) (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}) (1 + x + x^{2}) : x^{14} + 7 x^{13} + 28 x^{12} + 77 x^{11} + 161 x^{10} + 266 x^{9} + 357 x^{8} + 393 x^{7} + 357 x^{6} + 266 x^{5} + 161 x^{4} + 77 x^{3} + 28 x^{2} + 7 x + 1

= x^{14} + 7 x^{13} + 28 x^{12} + 77 x^{11} + 161 x^{10} + 266 x^{9} + 357 x^{8} + 393 x^{7} + 357 x^{6} + 266 x^{5} + 161 x^{4} + 77 x^{3} + 28 x^{2} + 7 x + 1

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

e x p an d sin (- \frac{π}{4}) sin (- \frac{π}{12})

e x p an d \frac{3 + x}{x ( x + 1 )}

e x p an d \frac{5 x ^{2} - 25 x + 20}{- 3 x ^{2} + 24 x - 48}

e x p an d \frac{( 0.13 + y ) ( y )}{0.13 - y}