erweitern ((6x^2-3)^4)/((2x^3+8)^5)

Lösung

erweitern

\frac{( 6 x ^{2} - 3 ) ^{4}}{( 2 x ^{3} + 8 ) ^{5}}

\frac{1296 x ^{8} - 2592 x ^{6} + 1944 x ^{4} - 648 x ^{2} + 81}{32 x ^{15} + 640 x ^{12} + 5120 x ^{9} + 20480 x ^{6} + 40960 x ^{3} + 32768}

Schritte zur Lösung

\frac{( 6 x ^{2} - 3 ) ^{4}}{( 2 x ^{3} + 8 ) ^{5}}

(2 x^{3} + 8)^{5} = 32 x^{15} + 640 x^{12} + 5120 x^{9} + 20480 x^{6} + 40960 x^{3} + 32768

= \frac{( 6 x ^{2} - 3 ) ^{4}}{32 x ^{15} + 640 x ^{12} + 5120 x ^{9} + 20480 x ^{6} + 40960 x ^{3} + 32768}

(6 x^{2} - 3)^{4} = 1296 x^{8} - 2592 x^{6} + 1944 x^{4} - 648 x^{2} + 81

= \frac{1296 x ^{8} - 2592 x ^{6} + 1944 x ^{4} - 648 x ^{2} + 81}{32 x ^{15} + 640 x ^{12} + 5120 x ^{9} + 20480 x ^{6} + 40960 x ^{3} + 32768}

e x p an d 3 (3 - 1)

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

e x p an d (3 - \frac{1}{3} x)^{5}

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

e x p an d (1 - i) (1 + i)