erweitern (x+x^2+x^3+x^4)^5

Lösung

erweitern

(x + x^{2} + x^{3} + x^{4})^{5}

x^{20} + 5 x^{19} + 15 x^{18} + 35 x^{17} + 65 x^{16} + 101 x^{15} + 135 x^{14} + 155 x^{13} + 155 x^{12} + 135 x^{11} + 101 x^{10} + 65 x^{9} + 35 x^{8} + 15 x^{7} + 5 x^{6} + x^{5}

Schritte zur Lösung

(x + x^{2} + x^{3} + x^{4})^{5}

(x + x^{2} + x^{3} + x^{4})^{5} = (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4})

= (x^{4} + x^{3} + x^{2} + x) (x^{4} + x^{3} + x^{2} + x) (x^{4} + x^{3} + x^{2} + x) (x^{4} + x^{3} + x^{2} + x) (x^{4} + x^{3} + x^{2} + x)

Multipliziere aus

(x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) (x + x^{2} + x^{3} + x^{4}) : x^{20} + 5 x^{19} + 15 x^{18} + 35 x^{17} + 65 x^{16} + 101 x^{15} + 135 x^{14} + 155 x^{13} + 155 x^{12} + 135 x^{11} + 101 x^{10} + 65 x^{9} + 35 x^{8} + 15 x^{7} + 5 x^{6} + x^{5}

= x^{20} + 5 x^{19} + 15 x^{18} + 35 x^{17} + 65 x^{16} + 101 x^{15} + 135 x^{14} + 155 x^{13} + 155 x^{12} + 135 x^{11} + 101 x^{10} + 65 x^{9} + 35 x^{8} + 15 x^{7} + 5 x^{6} + x^{5}

e x p an d (v + w + x + y + z)^{3}

e x p an d \frac{b}{s ^{2} \cdot ( s + a )}

s im pl i f y (3 x + 2 \circ 3 x^{2} + 2) (x)

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

e x p an d \frac{( x + 3 ) ( x + 5 )}{( x + 2 )}