erweitern (5x^4-6x^3+x)^5

Lösung

erweitern

(5 x^{4} - 6 x^{3} + x)^{5}

3125 x^{20} - 18750 x^{19} + 45000 x^{18} - 50875 x^{17} + 17400 x^{16} + 19224 x^{15} - 20350 x^{14} + 1980 x^{13} + 5400 x^{12} - 1910 x^{11} - 600 x^{10} + 360 x^{9} + 25 x^{8} - 30 x^{7} + x^{5}

Schritte zur Lösung

(5 x^{4} - 6 x^{3} + x)^{5}

(5 x^{4} - 6 x^{3} + x)^{5} = (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x)

= (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x)

Multipliziere aus

(5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) (5 x^{4} - 6 x^{3} + x) : 3125 x^{20} - 18750 x^{19} + 45000 x^{18} - 50875 x^{17} + 17400 x^{16} + 19224 x^{15} - 20350 x^{14} + 1980 x^{13} + 5400 x^{12} - 1910 x^{11} - 600 x^{10} + 360 x^{9} + 25 x^{8} - 30 x^{7} + x^{5}

= 3125 x^{20} - 18750 x^{19} + 45000 x^{18} - 50875 x^{17} + 17400 x^{16} + 19224 x^{15} - 20350 x^{14} + 1980 x^{13} + 5400 x^{12} - 1910 x^{11} - 600 x^{10} + 360 x^{9} + 25 x^{8} - 30 x^{7} + x^{5}

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

s im pl i f y (3 x - 2) (3 x + 2)

s im pl i f y (x + 10) (x - 10)

e x p an d (1 + e^{t})^{2}

e x p an d \frac{( 18 e ^{x} )}{( 3 e ^{x} + 6 ) ^{2}}