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

Lösung

erweitern

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

1024 x^{10} + 2560 x^{9} + 6400 x^{8} + 8960 x^{7} + 11840 x^{6} + 10592 x^{5} + 8880 x^{4} + 5040 x^{3} + 2700 x^{2} + 810 x + 243

Schritte zur Lösung

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

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

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

Multipliziere aus

(3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) : 1024 x^{10} + 2560 x^{9} + 6400 x^{8} + 8960 x^{7} + 11840 x^{6} + 10592 x^{5} + 8880 x^{4} + 5040 x^{3} + 2700 x^{2} + 810 x + 243

= 1024 x^{10} + 2560 x^{9} + 6400 x^{8} + 8960 x^{7} + 11840 x^{6} + 10592 x^{5} + 8880 x^{4} + 5040 x^{3} + 2700 x^{2} + 810 x + 243

e x p an d \frac{( u + 5 ) ( 24 u - 30 )}{4 u ^{4} - 25 u ^{2}}

e x p an d (x + 2) \cdot e^{x}

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

e x p an d \frac{4 x ^{2}}{( 1 - x ) ( 1 + x ^{2} ) ^{2}}

e x p an d \frac{1}{( x + 2 ) ( x + 3 )}