erweitern (x^6(x-6)^6)/((x^2+8)^6)

Lösung

erweitern

\frac{x ^{6} ( x - 6 ) ^{6}}{( x ^{2} + 8 ) ^{6}}

\frac{x ^{12} - 36 x ^{11} + 540 x ^{10} - 4320 x ^{9} + 19440 x ^{8} - 46656 x ^{7} + 46656 x ^{6}}{x ^{12} + 48 x ^{10} + 960 x ^{8} + 10240 x ^{6} + 61440 x ^{4} + 196608 x ^{2} + 262144}

Schritte zur Lösung

\frac{x ^{6} ( x - 6 ) ^{6}}{( x ^{2} + 8 ) ^{6}}

(x^{2} + 8)^{6} = x^{12} + 48 x^{10} + 960 x^{8} + 10240 x^{6} + 61440 x^{4} + 196608 x^{2} + 262144

= \frac{x ^{6} ( x - 6 ) ^{6}}{x ^{12} + 48 x ^{10} + 960 x ^{8} + 10240 x ^{6} + 61440 x ^{4} + 196608 x ^{2} + 262144}

(x - 6)^{6} = x^{6} - 36 x^{5} + 540 x^{4} - 4320 x^{3} + 19440 x^{2} - 46656 x + 46656

= \frac{x ^{6} ( x ^{6} - 36 x ^{5} + 540 x ^{4} - 4320 x ^{3} + 19440 x ^{2} - 46656 x + 46656 )}{x ^{12} + 48 x ^{10} + 960 x ^{8} + 10240 x ^{6} + 61440 x ^{4} + 196608 x ^{2} + 262144}

Multipliziere aus

x^{6} (x^{6} - 36 x^{5} + 540 x^{4} - 4320 x^{3} + 19440 x^{2} - 46656 x + 46656) : x^{12} - 36 x^{11} + 540 x^{10} - 4320 x^{9} + 19440 x^{8} - 46656 x^{7} + 46656 x^{6}

= \frac{x ^{12} - 36 x ^{11} + 540 x ^{10} - 4320 x ^{9} + 19440 x ^{8} - 46656 x ^{7} + 46656 x ^{6}}{x ^{12} + 48 x ^{10} + 960 x ^{8} + 10240 x ^{6} + 61440 x ^{4} + 196608 x ^{2} + 262144}

e x p an d \frac{160 x ^{6} + 50000 x ^{3}}{3 ( 2 x + 5 ) ^{5}}

e x p an d (- 7 3 x - 9 4 x + 2 x^{4}) d x

e x p an d \frac{( k + 2 ) ( 2 k + 3 ) ( 2 k + 5 )}{3}

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

e x p an d \frac{- 10 ( x + 3 ) ^{\frac{3}{2}} + 2 ( x + 3 ) ^{\frac{5}{2}}}{5}