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

Lösung

erweitern

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

1024 x^{10} + 3840 x^{9} + 8320 x^{8} + 12000 x^{7} + 12820 x^{6} + 10323 x^{5} + 6410 x^{4} + 3000 x^{3} + 1040 x^{2} + 240 x + 32

Schritte zur Lösung

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

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

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

Multipliziere aus

(2 + 3 x + 4 x^{2}) (2 + 3 x + 4 x^{2}) (2 + 3 x + 4 x^{2}) (2 + 3 x + 4 x^{2}) (2 + 3 x + 4 x^{2}) : 1024 x^{10} + 3840 x^{9} + 8320 x^{8} + 12000 x^{7} + 12820 x^{6} + 10323 x^{5} + 6410 x^{4} + 3000 x^{3} + 1040 x^{2} + 240 x + 32

= 1024 x^{10} + 3840 x^{9} + 8320 x^{8} + 12000 x^{7} + 12820 x^{6} + 10323 x^{5} + 6410 x^{4} + 3000 x^{3} + 1040 x^{2} + 240 x + 32

e x p an d 25 (2 - 3) 2 + 3

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

e x p an d \frac{7 ( 2 x + 1 )}{3 x - 5}

e x p an d - \frac{4}{( x - 1 ) ^{3}}

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