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

Lösung

erweitern

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

- 243 x^{10} - 810 x^{9} - 270 x^{8} + 1440 x^{7} + 840 x^{6} - 1232 x^{5} - 560 x^{4} + 640 x^{3} + 80 x^{2} - 160 x + 32

Schritte zur Lösung

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

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

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

Multipliziere aus

(2 - 2 x - 3 x^{2}) (2 - 2 x - 3 x^{2}) (2 - 2 x - 3 x^{2}) (2 - 2 x - 3 x^{2}) (2 - 2 x - 3 x^{2}) : - 243 x^{10} - 810 x^{9} - 270 x^{8} + 1440 x^{7} + 840 x^{6} - 1232 x^{5} - 560 x^{4} + 640 x^{3} + 80 x^{2} - 160 x + 32

= - 243 x^{10} - 810 x^{9} - 270 x^{8} + 1440 x^{7} + 840 x^{6} - 1232 x^{5} - 560 x^{4} + 640 x^{3} + 80 x^{2} - 160 x + 32

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

e x p an d - \frac{( s + 2 ) ( s + 3 ) ( s + 7 ) ( s + 10 )}{( s + 5 )}

e x p an d (x + y i)^{4}

e x p an d (4 x^{3} y - 15 x^{2} - y) d x + (x^{4} + 3 y^{2} - x) d y

e x p an d \frac{16}{( x ^{2} + 4 ) ^{2}}