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

Lösung

erweitern

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

x^{15} + 15 x^{14} + 90 x^{13} + 295 x^{12} + 705 x^{11} + 1593 x^{10} + 2950 x^{9} + 4275 x^{8} + 6750 x^{7} + 8000 x^{6} + 7500 x^{5} + 11250 x^{4} + 3125 x^{3} + 9375 x^{2} + 3125

Schritte zur Lösung

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

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

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

Multipliziere aus

(x^{3} + 3 x^{2} + 5) (x^{3} + 3 x^{2} + 5) (x^{3} + 3 x^{2} + 5) (x^{3} + 3 x^{2} + 5) (x^{3} + 3 x^{2} + 5) : x^{15} + 15 x^{14} + 90 x^{13} + 295 x^{12} + 705 x^{11} + 1593 x^{10} + 2950 x^{9} + 4275 x^{8} + 6750 x^{7} + 8000 x^{6} + 7500 x^{5} + 11250 x^{4} + 3125 x^{3} + 9375 x^{2} + 3125

= x^{15} + 15 x^{14} + 90 x^{13} + 295 x^{12} + 705 x^{11} + 1593 x^{10} + 2950 x^{9} + 4275 x^{8} + 6750 x^{7} + 8000 x^{6} + 7500 x^{5} + 11250 x^{4} + 3125 x^{3} + 9375 x^{2} + 3125

e x p an d \frac{27 \cdot ( s + 2 )}{2}

e x p an d T (x + 2 y + z, x + 2 z, x + y + 2 z)

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

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

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