erweitern ((2x^4+4x+1)(5x^2+3x+1))/((2x^2+5)^3)

Lösung

erweitern

\frac{( 2 x ^{4} + 4 x + 1 ) ( 5 x ^{2} + 3 x + 1 )}{( 2 x ^{2} + 5 ) ^{3}}

\frac{10 x ^{6} + 6 x ^{5} + 2 x ^{4} + 20 x ^{3} + 17 x ^{2} + 7 x + 1}{8 x ^{6} + 60 x ^{4} + 150 x ^{2} + 125}

Schritte zur Lösung

\frac{( 2 x ^{4} + 4 x + 1 ) ( 5 x ^{2} + 3 x + 1 )}{( 2 x ^{2} + 5 ) ^{3}}

(2 x^{2} + 5)^{3} = 8 x^{6} + 60 x^{4} + 150 x^{2} + 125

= \frac{( 2 x ^{4} + 4 x + 1 ) ( 5 x ^{2} + 3 x + 1 )}{8 x ^{6} + 60 x ^{4} + 150 x ^{2} + 125}

Multipliziere aus

(2 x^{4} + 4 x + 1) (5 x^{2} + 3 x + 1) : 10 x^{6} + 6 x^{5} + 2 x^{4} + 20 x^{3} + 17 x^{2} + 7 x + 1

= \frac{10 x ^{6} + 6 x ^{5} + 2 x ^{4} + 20 x ^{3} + 17 x ^{2} + 7 x + 1}{8 x ^{6} + 60 x ^{4} + 150 x ^{2} + 125}

e x p an d (s + a) \cdot (s + b) \cdot (s + c) \cdot (s + d) \cdot (s + e)

e x p an d (5 x^{2} + \frac{2}{x ^{4}} - 3 3 x) d x

e x p an d \frac{125 ( π + 200 )}{π}

e x p an d \frac{( x ^{5} + 3 ) ^{10}}{10}

e x p an d \frac{- 3}{3 ^{2} - 3 - 2}