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

Lösung

erweitern

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

y^{10} + 10 y^{9} + 55 y^{8} + 200 y^{7} + 530 y^{6} + 1052 y^{5} + 1590 y^{4} + 1800 y^{3} + 1485 y^{2} + 810 y + 243

Schritte zur Lösung

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

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

= (y^{2} + 2 y + 3) (y^{2} + 2 y + 3) (y^{2} + 2 y + 3) (y^{2} + 2 y + 3) (y^{2} + 2 y + 3)

Multipliziere aus

(3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) : y^{10} + 10 y^{9} + 55 y^{8} + 200 y^{7} + 530 y^{6} + 1052 y^{5} + 1590 y^{4} + 1800 y^{3} + 1485 y^{2} + 810 y + 243

= y^{10} + 10 y^{9} + 55 y^{8} + 200 y^{7} + 530 y^{6} + 1052 y^{5} + 1590 y^{4} + 1800 y^{3} + 1485 y^{2} + 810 y + 243

e x p an d \frac{3 s ^{3} + 4 s ^{2} + 36 s + 16}{( s ^{2} + 4 ) ( s ^{2} - 4 )}

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

e x p an d \frac{6 ( y - 3 )}{43}

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

e x p an d (y^{2} + x y^{3}) d x + (5 y^{2} - x y + y^{3} sin (y) d y)