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

Lösung

erweitern

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

\frac{1}{4 x ^{8} + 16 x ^{7} + 72 x ^{6} + 160 x ^{5} + 364 x ^{4} + 480 x ^{3} + 648 x ^{2} + 432 x + 324}

Schritte zur Lösung

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

(x^{2} + x + 3)^{4} = x^{8} + 4 x^{7} + 18 x^{6} + 40 x^{5} + 91 x^{4} + 120 x^{3} + 162 x^{2} + 108 x + 81

= \frac{1}{4 ( x ^{8} + 4 x ^{7} + 18 x ^{6} + 40 x ^{5} + 91 x ^{4} + 120 x ^{3} + 162 x ^{2} + 108 x + 81 )}

Multipliziere aus

4 (x^{8} + 4 x^{7} + 18 x^{6} + 40 x^{5} + 91 x^{4} + 120 x^{3} + 162 x^{2} + 108 x + 81) : 4 x^{8} + 16 x^{7} + 72 x^{6} + 160 x^{5} + 364 x^{4} + 480 x^{3} + 648 x^{2} + 432 x + 324

= \frac{1}{4 x ^{8} + 16 x ^{7} + 72 x ^{6} + 160 x ^{5} + 364 x ^{4} + 480 x ^{3} + 648 x ^{2} + 432 x + 324}

e x p an d \frac{35}{6 d ^{2} ( 18 d ^{2} - 11 d + 1 )}

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

e x p an d (6 x^{5} - 4 x^{3} + 2 x) d x

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

e x p an d \frac{( 50 - ln ( 5 ) ) ( 375 - 5 )}{140620}